PSTAT 100: Lecture 01

An Introduction to Data

Ethan P. Marzban

Department of Statistics and Applied Probability; UCSB

Summer Session A, 2025

Introduction

Welcome to the Course!

  • Welcome to PSTAT 100! I am so glad to be here on this journey with you.

  • About me: Ethan P. Marzban (he/him); rising 6th-Year PhD Student in the PSTAT Department

  • I am incredibly thankful to have Erika McPhillips (she/her) as a TA for this course!

Office Hours (subject to change):
Who? When? Where?
Ethan Wednesdays, 3:30 - 4:30 pm GIRV 2123
Fridays, 9:00 - 10:30 am Zoom
Erika Tuesdays, 4:15 - 5:15 pm SH 5421
Thursdays, 4:15 - 5:15 pm SH 5421

Course Logistics

Important Course Sites

  • There are three important sites related to the course:

    • Main Course Website: https://ucsb-pstat100.github.io
      This is where lecture slides will be posted, along with the course policies and the course schedule
    • Course Computing Server: Please See Canvas
      This is where all labs, homeworks, and project files will be posted. Please make sure to use the bit.ly link every time you need to access the course computing server.
    • Gradescope: https://www.gradescope.com/courses/995844
      This is where you will submit the majority of the assignments this quarter, and is also where you will be able to view your completed ICAs

Course Logistics

Course Policies

  • If you haven’t already, please read through the Course Policies fully.

    • They lay out policies surrounding late work, how your final grades will be computed, what constitutes allowable use of AI, and much more.
  • One highlight: you will be graded on labs, homeworks, projects, and in-class assessments.

    • The Course Policies provide further details on how these assignments differ, as well as how they factor in to your final course grade.

Some Tips for Success

  • Create a weekly schedule for yourself, and allocate a bit of time for PSTAT 100 each day.
    • E.g. for working on homework/projects, working through practice problems, reviewing notes, etc.
  • Take notes!
    • Course slides are somewhat comprehensive, but not the full story - I’ll often say things in class that are very important (and potentially testable on ICAs…)
  • Form Study Groups
    • Data Science is a highly collaborative field - get some practice forming these connections by connecting with your fellow classmates!

What Is Data Science?

Not Necessarily a Rhetorical Question!

Data Science

Your Thoughts, from the Google Form!

Data Science

The First “Expert”

  • Interdisciplinary; emphasis on domain knowledge

    • Draws from expertise and innovations from many fields
  • Data-Driven; collects, interprets, and uses data to say things about the world.

Data Science

The Second “Expert”

Data Science

Stats, Maths, and Computing

  • Notice that these three fields (loosely) correspond to the three prerequisites for this course!

Stats (PSTAT 120A)

  • Data has error and randomness; we need probability to be able to draw conclusions in the face of this randomness

Maths (MATH 4A)

  • Data is naturally expressible as matrices and vectors (more on this next week)

Computing (CMPSC 9/16)

  • Data is large, and often too complicated to handle by hand (without the aid of computing software)

Data Science

Still Very New!

Data Science Lifecycle

First Version

  • The Data Science Lifecycle (DSL) seeks to describe the general lifecycle of a typical data science project.

  • Four main stages: questioning, collecting, analyzing, and interpreting.

  • Lots of variations of the DSL, some with more steps than others.

  • Main idea: data science projects are highly iterative.

Data Science Lifecycle

Second Version

  • In my opinion, this is a much better representation of the DSL! (Though the graphic is certainly too complex.)

  • Again, data science is a highly iterative field; we rarely proceed in a linear fashion from start to finish.

    • Rather, we start, analyze out data, realize we need more data, collect more data, analyze our new data, realize we need to revise our original question, etc.

Data Science Lifecycle

Starting the Cycle

  • Sometimes we’ll begin with a question we want to answer.

  • E.g. “Has air quality in the US improved over time?”

  • E.g. “How has the distribution of wealth and income changed since the economic recession of 2008?”

Data Science Lifecycle

Starting the Cycle

  • In this case, our question will dictate what kind of data to collect
    • E.g. AQI data
    • E.g. Income Data; Federal Bank Data; etc.
  • In other cases, we’ll start with a dataset, which will then inform what question we want to ask.
    • Limitations in our dataset may also necessitate changes in our question; we’ll return to this point in a few lectures.

Data Science Lifecycle

Traveling Through the Cycle

  • Once we have our data, we need to analyze it.
  • This might involve data cleaning or data tidying; this could also involve producing appropriate visualizations.
    • At this stage, we may perform Exploratory Data Analysis (EDA).
    • In certain cases, we may find it useful to apply techniques from maching learning to better understand our dataset.

Data Science Lifecycle

Traveling Through the Cycle

  • Finally, we need to understand what our data is saying.
  • This will typically involve answering our question(s); oftentimes we’ll take things a step further and see if we can use our data to make sense of the world.
  • A key component of this stage of the DSL is producing some sort of a report or presentation.

PSTAT 100

  • We’ll be returning to the different stages of the DSL throughout this course (though not necessarily in order).
    • Consequently, I don’t expect you to understand all of the jargon on the previous few slides!
  • Today, we’ll start by addressing a question that is not explicitly part of the DSL, but implicitly forms the backbone of it: What is Data?

What Is Data?

What is Data?

What is Data?

  • According to Merriam-Webster (source), there are three definitions for data:
  1. factual information (such as measurements or statistics) used as a basis for reasoning, discussion, or calculation

  2. information in digital form that can be transmitted or processed

  3. information output by a sensing device or organ that includes both useful and irrelevant or redundant information and must be processed to be meaningful

  • I like the first definition, particularly the phrase “used as a basis for reasoning, discussion, or calculation.”

What is Data?

  • Raw data is often uninterpretable (and, in some cases, useless)

  • It’s the job of a Data Scientist to interpret the data, and use it to assess beliefs.

Definition

Data Literacy: “the ability to explore, understand, and communicate with data in a meaningful way.” (Tableau; source)

  • One of the goals of PSTAT 100 is to increase your data literacy.

  • We’ll develop a series of tools (that you will expound upon in your future PSTAT courses) in service of this goal.

A Dataset

Cats!

  • Let’s take a look at a concrete dataset.

  • This particular dataset was collected in 2013 by a collection veterinarians at The Royal Veterinary College in the United Kingdom.

    • The primary goal of the study was to investigate the prevalence of epilepsy in cats; for today, we’ll only be considering the characteristics of the cats included in the study.
  • Spend a few seconds taking in the dataset, and I’d like to know your initial reactions.

A Dataset

Cats!

 Cat.ID                   Breed        Age     Sex Neutered
      1     Domestic Short hair 14.7515400    Male Neutered
      2     Domestic Short hair 13.3305955    Male  Unknown
      3     Domestic Short hair 14.5270363  Female Neutered
      4     Domestic Short hair 14.8364134    Male Neutered
      5     Domestic Short hair 13.4154689  Female Neutered
      6     Domestic Short hair 12.5338809    Male  Unknown
      7     Domestic Short hair 12.3641342  Female Neutered
      8     Domestic Short hair  7.6522930    Male  Unknown
      9     Domestic Short hair 18.7515400    Male Neutered
     10     Domestic Short hair 11.2005476  Female Neutered
     11     Domestic Short hair 12.4298426  Female Neutered
     12     Domestic Short hair  7.5865845  Female Neutered
     13     Domestic Short hair  7.5865845  Female Neutered
     14     Domestic Short hair 17.3935661    Male  Unknown
     15     Domestic Short hair  7.7125257    Male Neutered
     16     Domestic Short hair 10.2313484    Male  Unknown
     17     Domestic Short hair  6.3709788  Female Neutered
     18     Domestic Short hair  6.4175222    Male Neutered
     19     Domestic Short hair  6.3463381  Female  Unknown
     20     Domestic Short hair  8.5968515  Female  Unknown
     21     Domestic Short hair  9.0704997  Female  Unknown
     22     Domestic Short hair  8.0657084  Female  Unknown
     23     Domestic Short hair  9.3305955    Male Neutered
     24     Domestic Short hair 10.6146475  Female Neutered
     25     Domestic Short hair 10.6146475    Male Neutered
     26     Domestic Short hair 10.9212868    Male Neutered
     27     Domestic Short hair 10.4421629  Female  Unknown
     28     Domestic Short hair 12.2491444    Male Neutered
     29     Domestic Short hair 10.2642026    Male Neutered
     30     Domestic Short hair 17.9301848  Female  Unknown
     31     Domestic Short hair 10.1656400  Female  Unknown
     32     Domestic Short hair 12.4845996    Male  Unknown
     33     Domestic Short hair 12.0876112    Male Neutered
     34     Domestic Short hair 12.6926762  Female Neutered
     35     Domestic Short hair 11.8110883  Female  Unknown
     36     Domestic Short hair 11.6988364    Male  Unknown
     37     Domestic Short hair 11.5838467    Male Neutered
     38     Domestic Short hair 11.6112252  Female  Unknown
     39     Domestic Short hair 10.7515400  Female Neutered
     40     Domestic Short hair 10.6694045    Male  Unknown
     41     Domestic Short hair 10.7351129    Male Neutered
     42     Domestic Short hair  7.6577687    Male  Unknown
     43     Domestic Short hair 13.4154689    Male  Unknown
     44     Domestic Short hair 22.7515400  Female Neutered
     45     Domestic Short hair 13.8343600  Female  Unknown
     46     Domestic Short hair 18.5845311  Female  Unknown
     47     Domestic Short hair 14.3874059    Male Neutered
     48     Domestic Short hair 17.4401095    Male  Unknown
     49     Domestic Short hair  9.4099932  Female  Unknown
     50     Domestic Short hair  8.3778234  Female  Unknown
     51     Domestic Short hair 15.1238877  Female Neutered
     52     Domestic Short hair  8.7008898  Female  Unknown
     53     Domestic Short hair 10.4175222  Female Neutered
     54     Domestic Short hair 10.4175222    Male Neutered
     55     Domestic Short hair 19.9370294  Female Neutered
     56     Domestic Short hair  9.8261465    Male Neutered
     57     Domestic Short hair 15.9972621    Male Neutered
     58     Domestic Short hair 19.4360027  Female Neutered
     59     Domestic Short hair 13.6673511  Female Neutered
     60     Domestic Short hair  9.0458590  Female  Unknown
     61     Domestic Short hair  6.9212868    Male  Unknown
     62     Domestic Short hair 15.9972621    Male  Unknown
     63     Domestic Short hair 19.7015743  Female Neutered
     64     Domestic Short hair 11.3319644  Female Neutered
     65     Domestic Short hair 19.8275154    Male Neutered
     66     Domestic Short hair 17.8015058    Male  Unknown
     67     Domestic Short hair  6.1464750  Female  Unknown
     68     Domestic Short hair 10.8062971  Female  Unknown
     69     Domestic Short hair 17.9986311  Female Neutered
     70      Domestic Long Hair 17.7631759    Male  Unknown
     71    Domestic Medium Hair  8.2710472  Female  Unknown
     72     Domestic Short hair  8.5886379  Female  Unknown
     73     Domestic Short hair  8.5886379    Male  Unknown
     74     Domestic Short hair  8.5886379  Female  Unknown
     75     Domestic Short hair  8.5886379  Female Neutered
     76     Domestic Short hair 13.9986311  Female  Unknown
     77     Domestic Short hair 18.9979466    Male  Unknown
     78     Domestic Short hair  7.4195756    Male Neutered
     79     Domestic Short hair  6.9158111    Male  Unknown
     80     Domestic Short hair  6.4175222  Female  Unknown
     81     Domestic Short hair 22.8583162    Male  Unknown
     82      Domestic Long Hair  6.6584531  Female  Unknown
     83      Domestic Long Hair  8.8815880    Male  Unknown
     84      Domestic Long Hair  8.8706366    Male  Unknown
     85    Domestic Medium Hair  6.7707050  Female  Unknown
     86 Domestic Semi Long Hair  5.8863792  Female  Unknown
     87 Domestic Semi Long Hair  5.8863792    Male Neutered
     88      Domestic Long Hair 15.3921971    Male  Unknown
     89      Domestic Long Hair 15.6796715  Female Neutered
     90    Domestic Medium Hair  9.8863792    Male  Unknown
     91      Domestic Long Hair  9.5222450  Female  Unknown
     92    Domestic Medium Hair 13.4565366    Male Neutered
     93 Domestic Semi Long Hair  7.5017112    Male  Unknown
     94      Domestic Long Hair  7.3921971  Female  Unknown
     95      Domestic Long Hair 14.2039699  Female  Unknown
     96      Domestic Long Hair  5.6208077    Male Neutered
     97 Domestic Semi Long Hair  5.8179329  Female Neutered
     98    Domestic Medium Hair  5.1718001    Male  Unknown
     99    Domestic Medium Hair  5.7549624  Female Neutered
    100      Domestic Long Hair  4.3559206    Male Neutered
    101     Domestic Short hair 11.7891855    Male Neutered
    102     Domestic Short hair  7.2662560  Female  Unknown
    103     Domestic Short hair 11.7262149  Female   Entire
    104     Domestic Short hair  5.6427105    Male Neutered
    105     Domestic Short hair 15.0828200  Female  Unknown
    106     Domestic Short hair 18.0835044  Female  Unknown
    107     Domestic Short hair 21.5003422  Female  Unknown
    108     Domestic Short hair 12.8186174  Female  Unknown
    109     Domestic Short hair 12.4982888  Female  Unknown
    110     Domestic Short hair 16.2628337  Female Neutered
    111     Domestic Short hair 13.5824778    Male Neutered
    112     Domestic Short hair 13.5824778    Male Neutered
    113     Domestic Short hair 16.6680356  Female Neutered
    114     Domestic Short hair 10.3490760  Female  Unknown
    115     Domestic Short hair  7.5592060    Male  Unknown
    116     Domestic Short hair  6.5325120  Female  Unknown
    117     Domestic Short hair  6.4175222    Male Neutered
    118     Domestic Short hair 13.1909651  Female Neutered
    119     Domestic Short hair  9.7440110    Male  Unknown
    120     Domestic Short hair 17.1882272  Female  Unknown
    121     Domestic Short hair 16.1642710    Male  Unknown
    122     Domestic Short hair  8.4845996    Male  Unknown
    123     Domestic Short hair 10.3134839  Female  Unknown
    124     Domestic Short hair 12.3011636  Female Neutered
    125     Domestic Short hair 14.8911704    Male  Unknown
    126     Domestic Short hair 13.6673511    Male  Unknown
    127     Domestic Short hair 12.2765229    Male  Unknown
    128     Domestic Short hair 17.4154689  Female  Unknown
    129     Domestic Short hair  6.8610541    Male  Unknown
    130     Domestic Short hair 13.9986311    Male Neutered
    131     Domestic Short hair 10.5434634  Female  Unknown
    132     Domestic Short hair 12.0821355  Female Neutered
    133     Domestic Short hair  7.5236140    Male  Unknown
    134     Domestic Short hair  7.5263518  Female Neutered
    135     Domestic Short hair  8.3668720  Female Neutered
    136     Domestic Short hair  7.4496920    Male  Unknown
    137     Domestic Short hair 20.4161533  Female  Unknown
    138     Domestic Short hair  6.4175222    Male Neutered
    139     Domestic Short hair 17.0102669    Male Neutered
    140     Domestic Short hair  9.3333333  Female Neutered
    141     Domestic Short hair  9.3333333  Female  Unknown
    142     Domestic Short hair  4.5475702    Male Neutered
    143     Domestic Short hair 10.7323751    Male  Unknown
    144     Domestic Short hair  9.4537988    Male  Unknown
    145    Domestic Medium Hair  9.7878166    Male  Unknown
    146      Domestic Long Hair 11.1375770    Male Neutered
    147    Domestic Medium Hair 13.8097194  Female  Unknown
    148                  Bengal  8.2299795    Male  Unknown
    149 Domestic Semi Long Hair  5.2375086    Male  Unknown
    150      Domestic Long Hair  4.3559206  Female Neutered
    151 Domestic Semi Long Hair  4.3285421    Male  Unknown
    152     Domestic Short hair 10.7460643    Male  Unknown
    153     Domestic Short hair  5.5989049    Male  Unknown
    154     Domestic Short hair  5.4893908    Male  Unknown
    155     Domestic Short hair  5.5906913  Female  Unknown
    156     Domestic Short hair  4.7255305    Male Neutered
    157     Domestic Short hair  4.7255305  Female  Unknown
    158     Domestic Short hair 12.2600958    Male  Unknown
    159     Domestic Short hair 10.3436003    Male Neutered
    160     Domestic Short hair  9.2484600  Female  Unknown
    161     Domestic Short hair  4.6105407    Male  Unknown
    162     Domestic Short hair  4.6680356    Male Neutered
    163     Domestic Short hair  4.6543463    Male Neutered
    164     Domestic Short hair  5.4291581  Female  Unknown
    165     Domestic Short hair  6.6447639  Female Neutered
    166     Domestic Short hair 17.8206708    Male  Unknown
    167     Domestic Short hair  8.4134155  Female  Unknown
    168     Domestic Short hair 10.0314853  Female Neutered
    169     Domestic Short hair 13.4647502    Male Neutered
    170     Domestic Short hair 10.9459274    Male Neutered
    171     Domestic Short hair  9.5879535  Female  Unknown
    172     Domestic Short hair  9.5879535    Male Neutered
    173     Domestic Short hair  8.7802875  Female  Unknown
    174     Domestic Short hair  8.5530459    Male Neutered
    175     Domestic Short hair  4.7665982  Female  Unknown
    176     Domestic Short hair  4.6160164    Male Neutered
    177     Domestic Short hair 11.4442163    Male Neutered
    178     Domestic Short hair  5.1362081  Female Neutered
    179     Domestic Short hair  7.3839836  Female  Unknown
    180     Domestic Short hair  4.4900753    Male Neutered
    181     Domestic Short hair 13.2292950  Female Neutered
    182     Domestic Short hair         NA    Male  Unknown
    183     Domestic Short hair  4.7173169  Female Neutered
    184     Domestic Short hair  4.3915127    Male Neutered
    185     Domestic Short hair 14.5023956    Male  Unknown
    186     Domestic Short hair 12.4982888  Female  Unknown
    187     Domestic Short hair 15.9972621  Female  Unknown
    188     Domestic Short hair 13.9986311    Male Neutered
    189     Domestic Short hair 15.7618070  Female  Unknown
    190     Domestic Short hair  6.4640657  Female Neutered
    191     Domestic Short hair  6.4175222    Male Neutered
    192     Domestic Short hair 10.4065708    Male  Unknown
    193     Domestic Short hair 12.7118412  Female  Unknown
    194     Domestic Short hair 11.9780972  Female Neutered
    195     Domestic Short hair  9.7522245    Male Neutered
    196     Domestic Short hair 13.6563997    Male  Unknown
    197     Domestic Short hair 17.5058179  Female Neutered
    198     Domestic Short hair 16.3778234    Male  Unknown
    199     Domestic Short hair 22.3408624    Male  Unknown
    200     Domestic Short hair  6.2039699  Female  Unknown
    201     Domestic Short hair  5.8015058    Male  Unknown
    202     Domestic Short hair  5.7385352    Male Neutered
    203     Domestic Short hair  4.7583847    Male Neutered
    204     Domestic Short hair  4.7227926    Male Neutered
    205     Domestic Short hair 16.9719370    Male  Unknown
    206     Domestic Short hair 16.3997262    Male  Unknown
    207     Domestic Short hair 16.3915127    Male  Unknown
    208     Domestic Short hair  4.3915127    Male Neutered
    209     Domestic Short hair  6.2067077    Male Neutered
    210     Domestic Short hair  8.2491444    Male  Unknown
    211     Domestic Short hair  4.6214921  Female Neutered
    212     Domestic Short hair  5.9466119    Male  Unknown
    213     Domestic Short hair 11.3949350    Male Neutered
    214     Domestic Short hair  5.5112936  Female  Unknown
    215     Domestic Short hair  4.7501711    Male  Unknown
    216     Domestic Short hair  4.4763860    Male  Unknown
    217     Domestic Short hair  8.5420945    Male Neutered
    218     Domestic Short hair  4.6872005    Male   Entire
    219     Domestic Short hair  4.7364819  Female Neutered
    220     Domestic Short hair  4.5995893    Male Neutered
    221     Domestic Short hair  6.9979466  Female Neutered
    222     Domestic Short hair  5.2867899  Female Neutered
    223     Domestic Short hair 14.8856947    Male Neutered
    224     Domestic Short hair  6.8939083    Male Neutered
    225     Domestic Short hair  4.6132786    Male Neutered
    226     Domestic Short hair  4.3750856    Male Neutered
    227     Domestic Short hair  4.3750856    Male  Unknown
    228     Domestic Short hair  4.4928131  Female Neutered
    229     Domestic Short hair  4.4572211  Female Neutered
    230     Domestic Short hair  4.5010267  Female  Unknown
    231     Domestic Short hair  4.5338809    Male  Unknown
    232     Domestic Short hair  4.5338809  Female Neutered
    233     Domestic Short hair 15.6687201  Female  Unknown
    234     Domestic Short hair 19.7508556    Male  Unknown
    235     Domestic Short hair 14.7515400    Male  Unknown
    236     Domestic Short hair 12.9117043    Male  Unknown
    237     Domestic Short hair 13.5824778    Male  Unknown
    238     Domestic Short hair 19.3100616    Male  Unknown
    239     Domestic Short hair  4.4763860  Female  Unknown
    240     Domestic Short hair  4.4599589    Male  Unknown
    241     Domestic Short hair  4.4763860    Male  Unknown
    242     Domestic Short hair  4.3312799    Male Neutered
    243     Domestic Short hair  6.7624914    Male  Unknown
    244     Domestic Short hair  4.3312799  Female Neutered
    245     Domestic Short hair 19.6687201    Male Neutered
    246     Domestic Short hair 13.9986311  Female  Unknown
    247     Domestic Short hair 15.1238877    Male Neutered
    248     Domestic Short hair 14.8062971    Male Neutered
    249     Domestic Short hair  9.7494867  Female  Unknown
    250     Domestic Short hair 13.7494867  Female  Unknown
    251     Domestic Short hair 15.7809719  Female  Unknown
    252     Domestic Short hair 15.7809719  Female  Unknown
    253     Domestic Short hair 15.9123888    Male Neutered
    254     Domestic Short hair 15.0663929    Male Neutered
    255     Domestic Short hair 13.5934292    Male Neutered
    256     Domestic Short hair 20.1642710    Male  Unknown
    257     Domestic Short hair 17.4154689  Female Neutered
    258     Domestic Short hair  6.6283368    Male Neutered
    259     Domestic Short hair  5.7166324  Female  Unknown
    260     Domestic Short hair  7.0527036  Female  Unknown
    261     Domestic Short hair  7.9972621    Male Neutered
    262     Domestic Short hair  6.1218344  Female  Unknown
    263     Domestic Short hair  9.0732375  Female  Unknown
    264     Domestic Short hair 13.3305955  Female Neutered
    265     Domestic Short hair 14.6694045    Male  Unknown
    266     Domestic Short hair 16.3312799    Male  Unknown
    267     Domestic Short hair 19.8357290    Male Neutered
    268     Domestic Short hair 13.7138946    Male  Unknown
    269     Domestic Short hair  7.6522930    Male  Unknown
    270     Domestic Short hair  9.8042437    Male  Unknown
    271     Domestic Short hair 11.2443532    Male  Unknown
    272     Domestic Short hair  8.3477070  Female Neutered
    273     Domestic Short hair 10.7515400    Male Neutered
    274     Domestic Short hair 10.4010951    Male Neutered
    275     Domestic Short hair 11.5017112    Male  Unknown
    276     Domestic Short hair 17.5058179    Male  Unknown
    277     Domestic Short hair  6.7597536    Male   Entire
    278     Domestic Short hair  7.4442163  Female  Unknown
    279     Domestic Short hair 14.2943190    Male Neutered
    280     Domestic Short hair  9.7741273    Male  Unknown
    281     Domestic Short hair  6.2833676    Male  Unknown
    282     Domestic Short hair  6.4010951  Female Neutered
    283     Domestic Short hair  4.7392197    Male Neutered
    284     Domestic Short hair  5.2648871  Female Neutered
    285     Domestic Short hair 15.6687201  Female  Unknown
    286     Domestic Short hair 15.6687201  Female  Unknown
    287      Domestic Long Hair 13.0568104    Male Neutered
    288      Domestic Long Hair 16.7337440    Male Neutered
    289 Domestic Semi Long Hair  9.1115674    Male Neutered
    290     Domestic Short hair  4.5037645  Female  Unknown
    291     Domestic Short hair  4.5037645    Male  Unknown
    292     Domestic Short hair  4.7036277  Female Neutered
    293     Domestic Short hair  4.5420945  Female  Unknown
    294     Domestic Short hair  4.4763860    Male  Unknown
    295     Domestic Short hair 14.7515400  Female Neutered
    296     Domestic Short hair 17.3305955    Male  Unknown
    297     Domestic Short hair 15.2498289    Male Neutered
    298     Domestic Short hair 14.5023956  Female  Unknown
    299     Domestic Short hair 17.5003422    Male Neutered
    300     Domestic Short hair 20.3312799    Male Neutered
    301     Domestic Short hair 21.9438741    Male  Unknown
    302     Domestic Short hair 11.3292266  Female  Unknown
    303     Domestic Short hair  9.4565366    Male Neutered
    304     Domestic Short hair 10.7214237  Female  Unknown
    305     Domestic Short hair  9.4264203    Male   Entire
    306     Domestic Short hair  9.4264203  Female   Entire
    307     Domestic Short hair  9.2922656  Female Neutered
    308     Domestic Short hair  9.9493498  Female Neutered
    309     Domestic Short hair 18.5462012  Female  Unknown
    310     Domestic Short hair 11.4989733  Female  Unknown
    311     Domestic Short hair 18.9130732  Female  Unknown
    312     Domestic Short hair 16.5831622    Male Neutered
    313     Domestic Short hair 11.7645448    Male Neutered
    314     Domestic Short hair 14.9979466  Female  Unknown
    315     Domestic Short hair  7.8576318    Male Neutered
    316 Domestic Semi Long Hair  5.1225188    Male  Unknown
    317      Domestic Long Hair 17.9137577    Male Neutered
    318     Domestic Short hair 16.8350445    Male Neutered
    319     Domestic Short hair  9.4893908  Female Neutered
    320     Domestic Short hair  7.5482546  Female Neutered
    321     Domestic Short hair  8.5886379  Female  Unknown
    322     Domestic Short hair  9.0622861    Male Neutered
    323     Domestic Short hair  6.5763176  Female  Unknown
    324     Domestic Short hair  6.5270363  Female Neutered
    325     Domestic Short hair  6.4421629    Male  Unknown
    326     Domestic Short hair  5.3141684  Female Neutered
    327    Domestic Medium Hair  5.9274470    Male Neutered
    328      Domestic Long Hair 17.8343600  Female Neutered
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    331    Domestic Medium Hair  6.3326489    Male Neutered
    332    Domestic Medium Hair  6.3326489    Male Neutered
    333      Domestic Long Hair  5.3141684    Male Neutered
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    335    Domestic Medium Hair  7.7837098    Male Neutered
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    337    Domestic Medium Hair 11.5920602    Male Neutered
    338    Domestic Medium Hair 11.4880219    Male Neutered
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    342     Domestic Short hair  7.7070500    Male  Unknown
    343     Domestic Short hair 18.5845311  Female  Unknown
    344     Domestic Short hair 18.2505133  Female Neutered
    345     Domestic Short hair 16.4490075  Female  Unknown
    346     Domestic Short hair 12.4079398    Male Neutered
    347     Domestic Short hair 11.4168378  Female Neutered
    348     Domestic Short hair 18.3956194  Female  Unknown
    349     Domestic Short hair  6.3874059  Female Neutered
    350     Domestic Short hair  6.1984942  Female  Unknown
    351     Domestic Short hair  8.4709103  Female  Unknown
    352     Domestic Short hair  9.3305955  Female  Unknown
    353     Domestic Short hair 13.7577002  Female  Unknown
    354     Domestic Short hair 14.2176591  Female  Unknown
    355     Domestic Short hair 11.5975359  Female  Unknown
    356     Domestic Short hair 17.9986311  Female  Unknown
    357     Domestic Short hair  6.8364134  Female Neutered
    358     Domestic Short hair 10.7652293  Female  Unknown
    359     Domestic Short hair 12.8459959  Female  Unknown
    360     Domestic Short hair  5.7686516  Female  Unknown
    361     Domestic Short hair 14.5023956  Female Neutered
    362     Domestic Short hair 14.5023956  Female Neutered
    363     Domestic Short hair  8.8213552  Female Neutered
    364     Domestic Short hair  6.3901437  Female Neutered
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    368      Domestic Long Hair 13.1088296  Female  Unknown
    369    Domestic Medium Hair  5.4318960  Female Neutered
    370      Domestic Long Hair  9.6563997    Male  Unknown
    371      Domestic Long Hair  5.0896646  Female  Unknown
    372      Domestic Long Hair 15.4168378  Female  Unknown
    373      Domestic Long Hair 12.9965777  Female Neutered
    374    Domestic Medium Hair 15.9123888  Female  Unknown
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    377     Domestic Short hair 16.8350445    Male  Unknown
    378     Domestic Short hair 14.5023956    Male  Unknown
    379     Domestic Short hair 15.9123888  Female Neutered
    380     Domestic Short hair 15.8357290  Female Neutered
    381     Domestic Short hair 16.8350445  Female  Unknown
    382     Domestic Short hair 16.7501711  Female Neutered
    383     Domestic Short hair  7.0444901  Female Neutered
    384     Domestic Short hair  4.5037645  Female  Unknown
    385     Domestic Short hair  4.1314168    Male Neutered
    386     Domestic Short hair  6.4120465  Female  Unknown
    387     Domestic Short hair 13.4072553    Male Neutered
    388     Domestic Short hair  9.0732375  Female  Unknown
    389     Domestic Short hair 13.5003422    Male Neutered
    390     Domestic Short hair  9.7850787    Male  Unknown
    391     Domestic Short hair  9.3607118    Male Neutered
    392     Domestic Short hair 10.5845311    Male Neutered
    393     Domestic Short hair 12.5503080  Female Neutered
    394     Domestic Short hair 19.5756331  Female  Unknown
    395     Domestic Short hair 13.1115674    Male  Unknown
    396     Domestic Short hair  6.7679671    Male  Unknown
    397     Domestic Short hair 15.9972621    Male  Unknown
    398      Domestic Long Hair  7.1622177  Female   Entire
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    400      Domestic Long Hair  6.2231348    Male  Unknown
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    402    Domestic Medium Hair 11.5592060    Male Neutered
    403    Domestic Medium Hair 14.2121834    Male  Unknown
    404     Domestic Short hair  4.4024641  Female  Unknown
    405     Domestic Short hair 16.4161533  Female Neutered
    406     Domestic Short hair 14.5023956    Male  Unknown
    407     Domestic Short hair 16.3312799    Male  Unknown
    408     Domestic Short hair 14.3326489  Female  Unknown
    409     Domestic Short hair 12.3312799  Female  Unknown
    410     Domestic Short hair 12.3312799    Male Neutered
    411     Domestic Short hair  4.9582478  Female Neutered
    412     Domestic Short hair 10.5845311    Male Neutered
    413     Domestic Short hair 10.6639288    Male  Unknown
    414      Domestic Long Hair 12.8761123    Male Neutered
    415    Domestic Medium Hair  6.5106092  Female  Unknown
    416    Domestic Medium Hair  6.5023956    Male  Unknown
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    418    Domestic Medium Hair  8.5639973  Female  Unknown
    419    Domestic Medium Hair 10.2422998    Male Neutered
    420 Domestic Semi Long Hair  5.5359343  Female  Unknown
    421 Domestic Semi Long Hair  5.5112936  Female  Unknown
    422      Domestic Long Hair 18.3080082    Male Neutered
    423      Domestic Long Hair 16.6680356    Male Neutered
    424      Domestic Long Hair 16.5256674    Male  Unknown
    425      Domestic Long Hair  6.4312115    Male  Unknown
    426    Domestic Medium Hair  8.3312799  Female  Unknown
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    428 Domestic Semi Long Hair  4.0520192    Male Neutered
    429      Domestic Long Hair  1.5003422    Male Neutered
    430     Domestic Short hair 12.8651608  Female Neutered
    431     Domestic Short hair 17.5003422  Female Neutered
    432     Domestic Short hair 15.5017112    Male  Unknown
    433     Domestic Short hair 14.5023956    Male Neutered
    434     Domestic Short hair 19.2498289    Male Neutered
    435     Domestic Short hair 19.4168378    Male Neutered
    436     Domestic Short hair 21.0157426  Female  Unknown
    437     Domestic Short hair  7.6522930    Male  Unknown
    438     Domestic Short hair 18.8939083  Female  Unknown
    439     Domestic Short hair  8.6269678    Male  Unknown
    440     Domestic Short hair  5.2867899  Female Neutered
    441     Domestic Short hair  8.3422313    Male Neutered
    442     Domestic Short hair  8.3422313  Female Neutered
    443     Domestic Short hair 10.8145106    Male  Unknown
    444     Domestic Short hair 19.6878850  Female  Unknown
    445     Domestic Short hair 21.3305955    Male  Unknown
    446     Domestic Short hair  3.6468172  Female Neutered
    447     Domestic Short hair 18.8829569  Female  Unknown
    448     Domestic Short hair 12.5475702    Male Neutered
    449     Domestic Short hair 13.0814511    Male  Unknown
    450     Domestic Short hair 11.4907598    Male  Unknown
    451     Domestic Short hair 18.2258727  Female  Unknown
    452     Domestic Short hair 20.2491444  Female  Unknown
    453     Domestic Short hair  4.0602327  Female  Unknown
    454     Domestic Short hair 19.9041752    Male Neutered
    455     Domestic Short hair  5.5989049    Male  Unknown
    456     Domestic Short hair 14.7515400  Female  Unknown
    457     Domestic Short hair 14.7515400    Male Neutered
    458     Domestic Short hair 11.9452430    Male Neutered
    459     Domestic Short hair  9.7494867  Female Neutered
    460 Domestic Semi Long Hair  5.5359343  Female  Unknown
    461    Domestic Medium Hair 10.9979466    Male Neutered
    462     Domestic Short hair 18.9979466  Female Neutered
    463     Domestic Short hair 11.2361396  Female  Unknown
    464     Domestic Short hair 10.6201232  Female  Unknown
    465     Domestic Short hair 10.4175222  Female Neutered
    466     Domestic Short hair  8.6433949    Male Neutered
    467     Domestic Short hair 17.5961670  Female  Unknown
    468     Domestic Short hair  7.5783710  Female  Unknown
    469     Domestic Short hair  5.5222450    Male Neutered
    470     Domestic Short hair  5.3032170    Male Neutered
    471     Domestic Short hair 16.8350445    Male Neutered
    472     Domestic Short hair  6.7241615    Male  Unknown
    473     Domestic Short hair  5.3305955  Female Neutered
    474     Domestic Short hair  6.9459274    Male  Unknown
    475     Domestic Short hair 17.2813142    Male Neutered
    476     Domestic Short hair  6.3901437    Male Neutered
    477     Domestic Short hair 12.8350445  Female Neutered
    478    Domestic Medium Hair 10.7077344    Male Neutered
    479 Domestic Semi Long Hair  3.4031485    Male Neutered
    480      Domestic Long Hair  3.4004107    Male Neutered
    481      Domestic Long Hair 12.9965777  Female  Unknown
    482     Domestic Short hair  5.7494867    Male Neutered
    483     Domestic Short hair 13.1635866    Male  Unknown
    484     Domestic Short hair  4.4900753  Female Neutered
    485     Domestic Short hair 15.0280630  Female  Unknown
    486     Domestic Short hair  4.1834360    Male  Unknown
    487     Domestic Short hair  4.2491444    Male Neutered
    488     Domestic Short hair 15.6687201    Male Neutered
    489     Domestic Short hair 14.4421629  Female Neutered
    490     Domestic Short hair 17.3744011    Male Neutered
    491     Domestic Short hair  9.8453114  Female Neutered
    492     Domestic Short hair  7.5482546    Male Neutered
    493     Domestic Short hair 18.7268994  Female Neutered
    494     Domestic Short hair  7.1348392    Male   Entire
    495     Domestic Short hair 13.8261465  Female  Unknown
    496     Domestic Short hair  6.6803559    Male  Unknown
    497     Domestic Short hair  6.2724162    Male Neutered
    498     Domestic Short hair  9.7248460  Female  Unknown
    499     Domestic Short hair  8.7255305    Male Neutered
    500     Domestic Short hair  8.7255305    Male  Unknown
    501     Domestic Short hair 19.9123888    Male  Unknown
    502     Domestic Short hair 13.4154689    Male  Unknown
    503     Domestic Short hair  6.2286105    Male  Unknown
    504     Domestic Short hair 10.5598905  Female  Unknown
    505     Domestic Short hair  4.7501711  Female Neutered
    506     Domestic Short hair  4.3203285  Female  Unknown
    507     Domestic Short hair 14.7515400  Female Neutered
    508     Domestic Short hair 10.0616016  Female  Unknown
    509     Domestic Short hair  9.6509240    Male Neutered
    510     Domestic Short hair 11.5373032    Male Neutered
    511     Domestic Short hair 11.5811088  Female  Unknown
    512                  Bengal  8.3942505  Female  Unknown
    513      Domestic Long Hair 11.5975359  Female  Unknown
    514      Domestic Long Hair 15.3182752  Female  Unknown
    515 Domestic Semi Long Hair  5.5879535  Female  Unknown
    516      Domestic Long Hair  5.4647502  Female Neutered
    517                  Bengal  4.9911020    Male Neutered
    518    Domestic Medium Hair  9.6563997  Female  Unknown
    519                  Bengal  4.6160164    Male Neutered
    520     Domestic Short hair 15.4168378  Female Neutered
    521     Domestic Short hair 16.1861739  Female  Unknown
    522     Domestic Short hair  8.2381930  Female Neutered
    523     Domestic Short hair 10.1054073    Male  Unknown
    524     Domestic Short hair  5.6290212  Female Neutered
    525     Domestic Short hair  6.0451745  Female Neutered
    526     Domestic Short hair 16.5831622  Female  Unknown
    527      Domestic Long Hair 16.1642710    Male Neutered
    528      Domestic Long Hair 21.4647502  Female Neutered
    529      Domestic Long Hair  5.6728268  Female  Unknown
    530    Domestic Medium Hair  5.1827515  Female  Unknown
    531    Domestic Medium Hair  5.1827515    Male Neutered
    532    Domestic Medium Hair 15.7563313    Male Neutered
    533    Domestic Medium Hair 15.7508556  Female  Unknown
    534      Domestic Long Hair 11.2361396  Female Neutered
    535                  Bengal  5.8124572    Male Neutered
    536      Domestic Long Hair  5.3223819    Male Neutered
    537      Domestic Long Hair 13.1635866    Male  Unknown
    538    Domestic Medium Hair  7.0444901  Female Neutered
    539      Domestic Long Hair 10.9979466  Female   Entire
    540    Domestic Medium Hair  5.9986311    Male Neutered
    541      Domestic Long Hair 16.4161533  Female Neutered
    542      Domestic Long Hair 11.5017112    Male Neutered
    543      Domestic Long Hair 13.5003422    Male  Unknown
    544      Domestic Long Hair 10.8555784    Male  Unknown
    545 Domestic Semi Long Hair  3.2498289  Female  Unknown
    546      Domestic Long Hair  5.7303217    Male  Unknown
    547     Domestic Short hair 17.7823409  Female  Unknown
    548     Domestic Short hair  5.2101300    Male Neutered
    549     Domestic Short hair 14.7515400  Female Neutered
    550     Domestic Short hair  7.8083504    Male  Unknown
    551     Domestic Short hair  8.7337440    Male  Unknown
    552     Domestic Short hair 12.5366188    Male  Unknown
    553     Domestic Short hair  4.9171800  Female Neutered
    554     Domestic Short hair  9.7494867  Female  Unknown
    555     Domestic Short hair 11.5208761  Female Neutered
    556     Domestic Short hair 11.4086242    Male Neutered
    557     Domestic Short hair 10.8555784  Female  Unknown
    558     Domestic Short hair 10.8555784  Female Neutered
    559     Domestic Short hair 14.5626283  Female Neutered
    560     Domestic Short hair 12.8706366  Female  Unknown
    561      Domestic Long Hair 19.3347023    Male Neutered
    562      Domestic Long Hair 14.9623546  Female  Unknown
    563    Domestic Medium Hair 11.1047228    Male Neutered
    564    Domestic Medium Hair 11.6933607    Male Neutered
    565    Domestic Medium Hair  3.4798084  Female  Unknown
    566    Domestic Medium Hair  8.6160164    Male  Unknown
    567      Domestic Long Hair  8.7282683  Female  Unknown
    568     Domestic Short hair  7.7262149    Male Neutered
    569     Domestic Short hair 23.2224504    Male Neutered
    570     Domestic Short hair 19.1622177    Male  Unknown
    571     Domestic Short hair  8.1587953  Female  Unknown
    572     Domestic Short hair 17.2484600  Female  Unknown
    573     Domestic Short hair 14.1930185    Male Neutered
    574     Domestic Short hair  2.3572895  Female  Unknown
    575     Domestic Short hair  2.3791923  Female Neutered
    576     Domestic Short hair  7.5728953    Male  Unknown
    577     Domestic Short hair  4.3039014  Female Neutered
    578     Domestic Short hair  4.1834360    Male  Unknown
    579     Domestic Short hair  9.0266940    Male  Unknown
    580     Domestic Short hair  8.5886379  Female Neutered
    581     Domestic Short hair  9.1635866    Male  Unknown
    582     Domestic Short hair 17.5961670    Male  Unknown
    583     Domestic Short hair  5.6728268  Female Neutered
    584     Domestic Short hair  5.4236824    Male Neutered
    585     Domestic Short hair 17.3305955    Male  Unknown
    586     Domestic Short hair 10.5845311    Male Neutered
    587     Domestic Short hair 14.7077344    Male Neutered
    588     Domestic Short hair  5.1362081  Female  Unknown
    589     Domestic Short hair 17.4154689    Male Neutered
    590     Domestic Short hair 13.9986311  Female  Unknown
    591     Domestic Short hair  2.3928816  Female Neutered
    592     Domestic Short hair 16.5694730  Female  Unknown
    593     Domestic Short hair 16.7501711    Male Neutered
    594     Domestic Short hair  9.4510609    Male Neutered
    595     Domestic Short hair 12.7501711    Male Neutered
    596     Domestic Short hair  1.5550992    Male  Unknown
    597     Domestic Short hair  2.9678303    Male  Unknown
    598     Domestic Short hair  3.6522930    Male Neutered
    599     Domestic Short hair  3.1649555  Female Neutered
    600     Domestic Short hair  3.2416153  Female  Unknown
    601     Domestic Short hair 16.3696099    Male   Entire
    602      Domestic Long Hair  8.6406571  Female Neutered
    603      Domestic Long Hair 17.2019165  Female  Unknown
    604      Domestic Long Hair  2.4394251  Female  Unknown
    605     Domestic Short hair 13.7494867  Female  Unknown
    606     Domestic Short hair 10.7652293  Female  Unknown
    607     Domestic Short hair 14.1382615  Female  Unknown
    608     Domestic Short hair 13.3771389  Female Neutered
    609     Domestic Short hair 20.0821355  Female  Unknown
    610     Domestic Short hair  9.4318960  Female Neutered
    611     Domestic Short hair 15.5154004  Female Neutered
    612     Domestic Short hair 16.3312799  Female Neutered
    613     Domestic Short hair 19.9780972  Female Neutered
    614     Domestic Short hair  6.1984942  Female Neutered
    615     Domestic Short hair  4.3778234  Female Neutered
    616     Domestic Short hair  5.3634497  Female Neutered
    617     Domestic Short hair 11.2553046  Female  Unknown
    618     Domestic Short hair 10.7652293  Female  Unknown
    619     Domestic Short hair  7.9972621  Female  Unknown
    620     Domestic Short hair  9.2156057  Female  Unknown
    621      Domestic Long Hair 10.6995209    Male Neutered
    622                   Other         NA Unknown   Entire
    623    Domestic Medium Hair  9.5112936    Male Neutered
    624      Domestic Long Hair 11.1594798  Female  Unknown
    625                   Other         NA Unknown   Entire
    626      Domestic Long Hair  7.4414784    Male Neutered
    627    Domestic Medium Hair  4.3696099    Male Neutered
    628      Domestic Long Hair 12.8021903  Female Neutered
    629                   Other         NA Unknown   Entire
    630      Domestic Long Hair 13.7494867  Female Neutered
    631      Domestic Long Hair  8.9965777  Female   Entire
    632      Domestic Long Hair  1.5030801    Male   Entire
    633     Domestic Short hair 16.4818617    Male Neutered
    634     Domestic Short hair         NA Unknown  Unknown
    635     Domestic Short hair  8.9363450    Male  Unknown
    636     Domestic Short hair  4.7693361  Female  Unknown
    637     Domestic Short hair  5.3579740  Female Neutered
    638     Domestic Short hair 16.5010267    Male Neutered
    639     Domestic Short hair 16.8350445  Female Neutered
    640     Domestic Short hair 14.8364134    Male  Unknown
    641     Domestic Short hair 20.4161533  Female  Unknown
    642     Domestic Short hair 16.5831622    Male  Unknown
    643     Domestic Short hair  6.9815195  Female  Unknown
    644     Domestic Short hair  9.5058179    Male Neutered
    645     Domestic Short hair 15.6331280    Male Neutered
    646     Domestic Short hair 10.6721424  Female  Unknown
    647     Domestic Short hair  8.6105407  Female  Unknown
    648     Domestic Short hair  1.5304586    Male Neutered
    649     Domestic Short hair  2.5598905    Male Neutered
    650     Domestic Short hair  3.5017112  Female  Unknown
    651     Domestic Short hair  8.7967146    Male Neutered
    652     Domestic Short hair  8.2929500    Male  Unknown
    653     Domestic Short hair  5.8863792    Male Neutered
    654     Domestic Short hair  1.2867899    Male Neutered
    655     Domestic Short hair  1.3552361    Male  Unknown
    656     Domestic Short hair 14.9979466    Male   Entire
    657     Domestic Short hair  4.8240931    Male  Unknown
    658     Domestic Short hair 15.5017112  Female Neutered
    659     Domestic Short hair 12.7392197    Male Neutered
    660     Domestic Short hair 12.7036277  Female Neutered
    661     Domestic Short hair  9.7111567    Male  Unknown
    662     Domestic Short hair  4.3066393    Male  Unknown
    663     Domestic Short hair  4.8405202    Male  Unknown
    664     Domestic Short hair  1.4428474    Male Neutered
    665     Domestic Short hair  1.3059548    Male  Unknown
    666     Domestic Short hair  8.0465435    Male   Entire
    667     Domestic Short hair  1.2867899    Male Neutered
    668     Domestic Short hair  1.3524983  Female  Unknown
    669     Domestic Short hair  1.3716632    Male  Unknown
    670    Domestic Medium Hair 17.5578371  Female  Unknown
    671      Domestic Long Hair         NA  Female   Entire
    672                   Other         NA Unknown  Unknown
    673     Domestic Short hair 13.6673511    Male Neutered
    674     Domestic Short hair  7.6030116  Female  Unknown
    675     Domestic Short hair 10.0999316  Female Neutered
    676     Domestic Short hair 12.9418207  Female  Unknown
    677     Domestic Short hair  9.8398357  Female  Unknown
    678     Domestic Short hair 10.6694045    Male  Unknown
    679     Domestic Short hair 19.4168378  Female Neutered
    680     Domestic Short hair 14.9130732  Female  Unknown
    681     Domestic Short hair  4.6269678  Female  Unknown
    682     Domestic Short hair  5.2484600  Female   Entire
    683     Domestic Short hair 15.8357290    Male  Unknown
    684     Domestic Short hair 14.4175222  Female Neutered
    685     Domestic Short hair  5.6700890    Male Neutered
    686     Domestic Short hair  4.5366188  Female Neutered
    687     Domestic Short hair 12.0219028    Male  Unknown
    688     Domestic Short hair  6.1218344    Male  Unknown
    689     Domestic Short hair  5.4154689  Female  Unknown
    690     Domestic Short hair 21.6673511  Female Neutered
    691     Domestic Short hair  8.6023272    Male  Unknown
    692     Domestic Short hair  4.8678987  Female Neutered
    693     Domestic Short hair 14.3846680    Male  Unknown
    694     Domestic Short hair 13.1006160  Female Neutered
    695     Domestic Short hair 15.3730322  Female Neutered
    696     Domestic Short hair  9.6043806    Male  Unknown
    697     Domestic Short hair  8.6023272  Female Neutered
    698     Domestic Short hair 12.8761123  Female Neutered
    699     Domestic Short hair  1.3497604  Female Neutered
    700     Domestic Short hair  4.7036277  Female  Unknown
    701     Domestic Short hair  1.0157426  Female Neutered
    702                  Bengal 14.5845311    Male  Unknown
    703                   Other  5.3661875  Female  Unknown
    704    Domestic Medium Hair 14.7159480    Male Neutered
    705     Domestic Short hair 21.6372348  Female  Unknown
    706     Domestic Short hair  3.3921971  Female Neutered
    707     Domestic Short hair  7.3237509    Male Neutered
    708     Domestic Short hair  9.9986311    Male Neutered
    709     Domestic Short hair  7.8384668    Male  Unknown
    710     Domestic Short hair  3.3648186    Male  Unknown
    711     Domestic Short hair  3.7234771    Male Neutered
    712     Domestic Short hair  4.2135524  Female Neutered
    713     Domestic Short hair  5.1800137    Male Neutered
    714     Domestic Short hair 15.6550308    Male  Unknown
    715     Domestic Short hair 12.3641342  Female Neutered
    716     Domestic Short hair  1.6071184    Male Neutered
    717     Domestic Short hair  6.8364134    Male  Unknown
    718     Domestic Short hair  2.5106092    Male Neutered
    719     Domestic Short hair  2.4996578    Male  Unknown
    720      Domestic Long Hair  9.6700890  Female  Unknown
    721    Domestic Medium Hair  2.4585900    Male Neutered
    722    Domestic Medium Hair 10.1081451    Male Neutered
    723 Domestic Semi Long Hair  8.4517454  Female Neutered
    724    Domestic Medium Hair 16.4380561    Male Neutered
    725      Domestic Long Hair 10.5023956    Male Neutered
    726 Domestic Semi Long Hair  4.2436687  Female Neutered
    727      Domestic Long Hair  3.3155373  Female   Entire
    728      Domestic Long Hair 18.1464750  Female  Unknown
    729    Domestic Medium Hair  3.2251882    Male  Unknown
    730      Domestic Long Hair 15.5619439    Male Neutered
    731    Domestic Medium Hair  1.5687885    Male Neutered
    732    Domestic Medium Hair  1.3114305    Male  Unknown
    733      Domestic Long Hair 14.7871321  Female  Unknown
    734    Domestic Medium Hair  0.8993694    Male   Entire
    735    Domestic Medium Hair  0.8268309    Male   Entire
    736 Domestic Semi Long Hair  1.2621492  Female Neutered
    737     Domestic Short hair 16.7830253  Female  Unknown
    738     Domestic Short hair  8.7693361  Female  Unknown
    739     Domestic Short hair  7.7344285  Female  Unknown
    740     Domestic Short hair  1.1800137    Male  Unknown
    741     Domestic Short hair  5.9110198 Unknown  Unknown
    742     Domestic Short hair  3.4086242  Female  Unknown
    743     Domestic Short hair  1.4483231    Male  Unknown
    744     Domestic Short hair  1.3196441    Male Neutered
    745     Domestic Short hair  5.9000684    Male   Entire
    746     Domestic Short hair  1.6536619    Male  Unknown
    747     Domestic Short hair  1.2621492    Male  Unknown
    748     Domestic Short hair  1.3880903  Female Neutered
    749     Domestic Short hair  1.3004791    Male  Unknown
    750     Domestic Short hair  1.4291581    Male   Entire
    751     Domestic Short hair  5.8809035    Male  Unknown
    752     Domestic Short hair  1.2813142    Male  Unknown
    753     Domestic Short hair 11.8494182  Female Neutered
    754     Domestic Short hair 11.7727584  Female Neutered
    755     Domestic Short hair  5.9739904    Male  Unknown
    756     Domestic Short hair  4.4490075  Female Neutered
    757     Domestic Short hair  4.1095140  Female Neutered
    758     Domestic Short hair 12.6954141    Male  Unknown
    759     Domestic Short hair  6.2669405  Female Neutered
    760     Domestic Short hair 14.4175222  Female Neutered
    761     Domestic Short hair  0.9719370    Male   Entire
    762     Domestic Short hair  1.1827515    Male   Entire
    763     Domestic Short hair 13.2375086    Male Neutered
    764     Domestic Short hair 11.3319644    Male Neutered
    765     Domestic Short hair  1.3990418    Male  Unknown
    766      Domestic Long Hair 12.7967146  Female Neutered
    767     Domestic Short hair  7.4031485  Female  Unknown
    768     Domestic Short hair  7.4031485  Female Neutered
    769     Domestic Short hair  7.2744695  Female  Unknown
    770     Domestic Short hair         NA  Female Neutered
    771     Domestic Short hair 14.9979466    Male Neutered
    772     Domestic Short hair  2.4394251  Female  Unknown
    773     Domestic Short hair  6.7816564    Male Neutered
    774     Domestic Short hair  5.8343600    Male  Unknown
    775     Domestic Short hair  5.8343600    Male  Unknown
    776     Domestic Short hair  7.7891855  Female  Unknown
    777     Domestic Short hair 11.5427789    Male  Unknown
    778     Domestic Short hair 13.1170431    Male  Unknown
    779     Domestic Short hair  2.6119097    Male Neutered
    780     Domestic Short hair  4.3559206    Male  Unknown
    781     Domestic Short hair 10.9158111    Male Neutered
    782     Domestic Short hair  8.6707734  Female  Unknown
    783     Domestic Short hair  6.5763176  Female  Unknown
    784     Domestic Short hair  3.8932238  Female  Unknown
    785     Domestic Short hair 20.9117043    Male  Unknown
    786     Domestic Short hair 11.8658453  Female  Unknown
    787     Domestic Short hair  1.2648871  Female  Unknown
    788     Domestic Short hair  5.9110198    Male Neutered
    789     Domestic Short hair  7.4140999    Male Neutered
    790     Domestic Short hair  2.6639288  Female  Unknown
    791     Domestic Short hair  2.9596167  Female  Unknown
    792     Domestic Short hair 18.4503765    Male  Unknown
    793     Domestic Short hair  3.6057495  Female  Unknown
    794     Domestic Short hair  1.4565366    Male Neutered
    795     Domestic Short hair 13.4839151  Female  Unknown
    796     Domestic Short hair 13.4839151  Female Neutered
    797     Domestic Short hair 16.5831622    Male Neutered
    798     Domestic Short hair  8.7036277  Female Neutered
    799     Domestic Short hair 15.4168378  Female  Unknown
    800     Domestic Short hair 15.8357290  Female Neutered
    801     Domestic Short hair 10.7515400  Female Neutered
    802     Domestic Short hair  5.1663244  Female Neutered
    803     Domestic Short hair 11.2991102  Female  Unknown
    804     Domestic Short hair  4.6379192  Female Neutered
    805     Domestic Short hair  2.7515400    Male  Unknown
    806     Domestic Short hair  1.5304586    Male Neutered
    807     Domestic Short hair  2.4010951  Female Neutered
    808     Domestic Short hair         NA    Male  Unknown
    809     Domestic Short hair  2.1081451  Female Neutered
    810     Domestic Short hair 16.8377823    Male Neutered
    811     Domestic Short hair  1.2855798    Male Neutered
    812     Domestic Short hair         NA  Female Neutered
    813     Domestic Short hair  0.9707322  Female   Entire
    814     Domestic Short hair  0.9707299  Female   Entire
    815     Domestic Short hair  0.9707004  Female  Unknown
    816     Domestic Short hair  6.0971937  Female   Entire
    817     Domestic Short hair  6.5790554  Female Neutered
    818     Domestic Short hair  3.2443532    Male Neutered
    819     Domestic Short hair  0.9281314  Female  Unknown
    820     Domestic Short hair  1.3744011    Male Neutered
    821     Domestic Short hair 18.3928816  Female Neutered
    822     Domestic Short hair  5.0184805  Female  Unknown
    823     Domestic Short hair  3.2114990    Male Neutered
    824     Domestic Short hair  0.9707026  Female   Entire
    825     Domestic Short hair  0.9719370  Female  Unknown
    826     Domestic Short hair  1.5304586    Male  Unknown
    827     Domestic Short hair  8.2819986  Female  Unknown
    828     Domestic Short hair 14.8364134  Female  Unknown
    829     Domestic Short hair  7.5674196  Female Neutered
    830     Domestic Short hair  3.9041752    Male  Unknown
    831     Domestic Short hair  3.8850103    Male  Unknown
    832     Domestic Short hair  7.7371663    Male Neutered
    833     Domestic Short hair  3.4880219    Male Neutered
    834     Domestic Short hair  7.4140999  Female  Unknown
    835     Domestic Short hair  4.2655715    Male  Unknown
    836     Domestic Short hair  8.4626968    Male  Unknown
    837     Domestic Short hair  8.7337440    Male  Unknown
    838     Domestic Short hair  2.5106092  Female  Unknown
    839     Domestic Short hair 16.7748118    Male   Entire
    840     Domestic Short hair  1.3470226  Female Neutered
    841     Domestic Short hair  1.3086927  Female Neutered
    842     Domestic Short hair  0.9034908  Female  Unknown
    843     Domestic Short hair  0.9226557    Male  Unknown
    844     Domestic Short hair  3.3073238    Male  Unknown
    845     Domestic Short hair 11.1786448  Female  Unknown
    846     Domestic Short hair 11.6687201    Male Neutered
    847     Domestic Short hair  4.0602327    Male  Unknown
    848     Domestic Short hair  0.7857632  Female   Entire
    849     Domestic Short hair  7.7316906    Male Neutered
    850     Domestic Short hair 11.7207392    Male Neutered
    851     Domestic Short hair 10.6885695    Male Neutered
    852     Domestic Short hair  3.6878850  Female  Unknown
    853     Domestic Short hair  2.6885695  Female Neutered
    854     Domestic Short hair  3.2498289  Female  Unknown
    855     Domestic Short hair  7.6960986    Male Neutered
    856     Domestic Short hair 15.8877481    Male  Unknown
    857     Domestic Short hair  4.8651608    Male  Unknown
    858     Domestic Short hair  1.9603012  Female  Unknown
    859     Domestic Short hair  6.3737166    Male  Unknown
    860     Domestic Short hair  6.7926078  Female Neutered
    861     Domestic Short hair 15.5017112    Male Neutered
    862     Domestic Short hair 10.1984942  Female  Unknown
    863     Domestic Short hair  2.6119097    Male  Unknown
    864     Domestic Short hair  2.5489391    Male  Unknown
    865     Domestic Short hair  2.4996578    Male Neutered
    866     Domestic Short hair 11.7919233  Female Neutered
    867     Domestic Short hair 12.8733744    Male Neutered
    868     Domestic Short hair  6.8227242    Male  Unknown
    869     Domestic Short hair 19.3812457  Female Neutered
    870     Domestic Short hair  1.1800137  Female Neutered
    871     Domestic Short hair 14.9075975  Female Neutered
    872     Domestic Short hair  1.5742642  Female Neutered
    873     Domestic Short hair  1.4072553  Female  Unknown
    874     Domestic Short hair  1.7385352    Male Neutered
    875     Domestic Short hair  1.6481862    Male Neutered
    876     Domestic Short hair  1.4620123  Female  Unknown
    877     Domestic Short hair  1.8672142    Male  Unknown
    878     Domestic Short hair  3.8576318  Female  Unknown
    879     Domestic Short hair  3.8576318    Male  Unknown
    880     Domestic Short hair  4.3504449    Male  Unknown
    881     Domestic Short hair 10.6803559    Male  Unknown
    882     Domestic Short hair  2.9596167  Female Neutered
    883     Domestic Short hair  3.9972621    Male  Unknown
    884     Domestic Short hair 11.1238877  Female  Unknown
    885     Domestic Short hair  4.9746749    Male Neutered
    886     Domestic Short hair  9.3305955    Male Neutered
    887     Domestic Short hair 16.1642710  Female  Unknown
    888     Domestic Short hair 18.6694045    Male Neutered
    889     Domestic Short hair 12.5338809  Female Neutered
    890     Domestic Short hair 13.5003422  Female  Unknown
    891     Domestic Short hair  5.3935661    Male  Unknown
    892     Domestic Short hair 19.5017112  Female Neutered
    893     Domestic Short hair  1.7138946    Male  Unknown
    894     Domestic Short hair 16.5831622  Female  Unknown
    895     Domestic Short hair 15.8850103    Male  Unknown
    896     Domestic Short hair 11.7043121    Male Neutered
    897     Domestic Short hair  2.4804928    Male Neutered
    898     Domestic Short hair  2.4668036    Male  Unknown
    899     Domestic Short hair  2.7679671  Female  Unknown
    900     Domestic Short hair  1.3497604  Female  Unknown
    901     Domestic Short hair         NA    Male Neutered
    902     Domestic Short hair  1.8206708  Female  Unknown
    903     Domestic Short hair  9.6673511  Female  Unknown
    904     Domestic Short hair  2.4010951  Female   Entire
    905     Domestic Short hair         NA    Male Neutered
    906     Domestic Short hair  0.8925394    Male  Unknown
    907     Domestic Short hair 17.7686516  Female Neutered
    908     Domestic Short hair 12.8952772  Female Neutered
    909     Domestic Short hair 12.9117043    Male  Unknown
    910     Domestic Short hair  3.4688569  Female  Unknown
    911     Domestic Short hair  3.3785079    Male   Entire
    912     Domestic Short hair  3.5592060    Male Neutered
    913     Domestic Short hair  3.5592060  Female  Unknown
    914     Domestic Short hair  5.6618754  Female Neutered
    915     Domestic Short hair  8.2464066  Female  Unknown
    916     Domestic Short hair  2.2477755  Female   Entire
    917     Domestic Short hair 22.7433265  Female  Unknown
    918     Domestic Short hair  2.7351129  Female  Unknown
    919     Domestic Short hair  1.2265572  Female Neutered
    920     Domestic Short hair 13.7494867    Male  Unknown
    921     Domestic Short hair 11.1156742  Female  Unknown
    922     Domestic Short hair  5.3086927  Female Neutered
    923     Domestic Short hair  1.3470226  Female Neutered
    924     Domestic Short hair  1.5003422    Male  Unknown
    925     Domestic Short hair  4.8213552  Female  Unknown
    926     Domestic Short hair  2.8199863  Female  Unknown
    927     Domestic Short hair         NA    Male   Entire
    928     Domestic Short hair  2.3326489    Male  Unknown
    929     Domestic Short hair  5.7494867  Female  Unknown
    930     Domestic Short hair  4.3367556    Male  Unknown
    931     Domestic Short hair  3.5592060  Female Neutered
    932     Domestic Short hair 10.2368241    Male  Unknown
    933     Domestic Short hair  3.7919233  Female Neutered
    934     Domestic Short hair  6.2614648    Male  Unknown
    935     Domestic Short hair  5.2210815  Female  Unknown
    936     Domestic Short hair 12.2108145  Female  Unknown
    937     Domestic Short hair  0.7857632  Female  Unknown
    938     Domestic Short hair  2.7433265  Female Neutered
    939     Domestic Short hair  0.8925394    Male  Unknown
    940     Domestic Short hair 13.2073922    Male  Unknown
    941    Domestic Medium Hair  9.3771389  Female Neutered
    942 Domestic Semi Long Hair  4.3668720  Female Neutered
    943      Domestic Long Hair 11.3264887  Female Neutered
    944 Domestic Semi Long Hair  1.4401095    Male  Unknown
    945 Domestic Semi Long Hair  9.2648871  Female Neutered
    946      Domestic Long Hair  3.5592060  Female  Unknown
    947                  Bengal  2.4503765  Female  Unknown
    948      Domestic Long Hair  2.5598905  Female Neutered
    949    Domestic Medium Hair 21.5441478  Female  Unknown
    950 Domestic Semi Long Hair  1.4537988  Female Neutered
    951    Domestic Medium Hair  1.5085558  Female   Entire
    952                 Burmese  4.3394935    Male  Unknown
    953                 Burmese  1.1060917  Female  Unknown
    954                 Burmese 16.9171800    Male Neutered
    955                 Burmese 14.9924709  Female Neutered
    956     Domestic Short hair  2.6830938    Male Neutered
    957     Domestic Short hair 11.8986995    Male   Entire
    958     Domestic Short hair  3.9123888  Female  Unknown
    959     Domestic Short hair  1.7193703    Male Neutered
    960     Domestic Short hair  1.4373717  Female Neutered
    961     Domestic Short hair  6.2669405    Male Neutered
    962     Domestic Short hair 11.6824093    Male Neutered
    963     Domestic Short hair 18.6694045    Male Neutered
    964     Domestic Short hair         NA  Female  Unknown
    965     Domestic Short hair  8.5065024  Female  Unknown
    966     Domestic Short hair 15.2826831    Male  Unknown
    967     Domestic Short hair  6.8418891    Male  Unknown
    968     Domestic Short hair  2.0944559  Female Neutered
    969     Domestic Short hair  1.1772758    Male Neutered
    970     Domestic Short hair  2.2505133    Male Neutered
    971     Domestic Short hair  9.8234086    Male  Unknown
    972                  Moggie  7.8329911  Female  Unknown
    973     Domestic Short hair         NA    Male  Unknown
    974     Domestic Short hair         NA    Male  Unknown
    975     Domestic Short hair  1.2292950  Female  Unknown
    976     Domestic Short hair  6.8062971  Female Neutered
    977     Domestic Short hair  1.8015058  Female Neutered
    978     Domestic Short hair  7.2908966    Male  Unknown
    979     Domestic Short hair  1.6235455    Male   Entire
    980     Domestic Short hair         NA    Male  Unknown
    981     Domestic Short hair  0.8925394  Female  Unknown
    982     Domestic Short hair  5.7768652    Male Neutered
    983     Domestic Short hair  7.3292266  Female Neutered
    984     Domestic Short hair  3.6002738    Male  Unknown
    985                 Burmese 10.5735797    Male  Unknown
    986      British Short Hair  3.2772074  Female Neutered
    987                 Burmese 13.6673511    Male  Unknown
    988                 Burmese  6.6228611    Male  Unknown
    989      British Short Hair  2.8802190    Male  Unknown
    990                 Ragdoll  3.6605065    Male  Unknown
    991      British Short Hair 11.2580424  Female Neutered
    992                 Ragdoll  3.4469541    Male Neutered
    993                Siberian  2.1738535    Male Neutered
    994     Domestic Short hair 12.2381930  Female  Unknown
    995     Domestic Short hair  6.7268994    Male  Unknown
    996     Domestic Short hair  2.7077344  Female Neutered
    997     Domestic Short hair  2.3983573    Male  Unknown
    998     Domestic Short hair  8.1040383    Male  Unknown
    999     Domestic Short hair  1.8398357    Male  Unknown
   1000     Domestic Short hair  1.5085558  Female Neutered
 [ reached 'max' / getOption("max.print") -- omitted 284547 rows ]

Cats Dataset

Initial Thoughts

  • On the one hand, we could make some observations about how the data is displayed
    • For example, it’s a pretty big dataset (I even had to truncate the output so that it fits in this presentation!)
    • The entries are displayed tabularly (sometimes called “rectangularly”)
  • On the other, we could make observations about what the data is saying
    • Each row represents information about a particular cat
    • From each cat, we have information on a series of attributes (sex, age, etc.)

Semantics vs. Structure

  • In general, we distinguish between the semantics and structure of a particular dataset.

  • The semantics of a dataset relate to the meaning behind the data.

    • What is the data trying to tell us?
  • The structure of a dataset pertains to how the data is displayed or organized.

    • How is the data telling us what it is telling us?
  • We’ll focus on data semantics for today, and return to the topic of data structure tomorrow.

Data Semantics

Definition

Definition: Data

We define an observation to be a collection of values measured on certain attributes (aka variables). From a semantic standpoint, we define data to be a collection of observations collected on observational units.

Cats Dataset

Semantics

 Cat.ID               Breed      Age    Sex Neutered
      1 Domestic Short hair 14.75154   Male Neutered
      2 Domestic Short hair 13.33060   Male  Unknown
      3 Domestic Short hair 14.52704 Female Neutered
      4 Domestic Short hair 14.83641   Male Neutered
 [ reached 'max' / getOption("max.print") -- omitted 285543 rows ]

Example Observation:

There was a 14.75154-year old Neutered Male Domestic Short Hair Cat, whose ID was 1.

Cats Dataset

Semantics

There was a cat whose ID was 1, whose breed was “Domestic Short hair”, whose age was 14.75154, whose sex was “Male”, and whose Neutered status was “Neutered”.

  • Variables: ID, Breed, Age, Sex, Neutered Status

There was a cat whose ID was 1, whose breed was “Domestic Short hair”, whose age was 14.75154, whose sex was “Male”, and whose Neutered status was “Neutered”.

  • Values: (1, “Domestic Short hair”, 14.75154, “Male”, “Neutered”)

Data Semantics

Observational Units

  • When trying to identify the observational units of a particular dataset, I like to ask myself the question: “if I were to replicate this data (i.e. re-collect it myself), what object/item would I actually observe/take measurements on?”
    • For example, if I wanted to replicate the cats dataset, I would need to start by collecting a bunch of cats, on which I could take measurements of whatever attributes I want.
  • Note that observational units aren’t always living entities; we could imagine a dataset in which countries are the observational units (e.g. we could measure various attributes - like GDP, life expectancy, etc. - about the different countries of the world)

Another Dataset

Undergraduate PSTAT Course Enrollments

      Course               Title S25 W25 F24 M24 S24 W24 F23 M23 S23 W23 F22
    PSTAT 5A  UNDERSTANDING DATA 167 222 213  76 258 283 549 110 212 279 499
    PSTAT 5H          STATISTICS  11  14  30  NA  31  24  25  NA  31  22   4
   PSTAT 5LS  STAT LIFE SCIENCES 355 340 348  59 304 299  NA  39 299 294  NA
     PSTAT 8  TRANS DS PROB STAT  70 105 137  22  83 134 132  18  86 156  70
    PSTAT 10  DATA SCIENCE PRINC 235 241 286  93 234 260 285  83 240 282 257
    PSTAT 99 INDEPENDENT STUDIES   1   2  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 100        DS_CONC&ANLS 109 131 108  NA  95  NA 104  48 125 127  NA
   PSTAT 105  INTRO N-PARAM METH  NA  79  NA  NA  NA  NA  39  NA  NA  NA  79
   PSTAT 109 STATISTICS FOR ECON  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 115 BAYES DATA ANALYSIS  81  56  74  25  74  96  16  15  38  70  63
  PSTAT 120A   PROB & STATISTICS 310 383 345  75 367 372 419  86 237 246 419
  PSTAT 120B   PROB & STATISTICS 312 329 236 136 382 241 261 102 256 256 165
  PSTAT 120C   PROB & STATISTICS 163  NA  37 129 131  39  19  81  65  31  87
   PSTAT 122 DESIGN OF EXPERMNTS 240 210 201  NA 177 162 167  NA 194 187 182
   PSTAT 123  SAMPLING TECHNIQUE  NA  NA  NA  NA  NA 137  NA  NA  NA  NA  NA
   PSTAT 126 REGRESSION ANALYSIS 197 214 272  94 147 200 123  84 149 175 182
   PSTAT 127    ADV STATS MODELS  NA  NA  72  NA  NA  NA  57  NA  NA  73  NA
   PSTAT 130    SAS BASE PROGRAM 116 120 121 108 122  97 120  95 119  98  97
   PSTAT 131  STAT MACHINE LEARN  96 156  64  80  93 138 150  55 108 197 178
   PSTAT 132 DATABASES FOR STATS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 134   STAT DATA SCIENCE  46  91  78  NA  70  78  80  NA  87  42  33
   PSTAT 135  BIG DATA ANALYTICS  96  NA  NA  NA  NA  99  NA  NA  NA  93  NA
   PSTAT 140 STATISTICAL PROCESS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 160A  STOCHASTIC PROCESS 132 217 126  NA 100 153 132  NA 108 161 184
  PSTAT 160B  STOCHASTIC PROCESS 116  77  86  NA 106  73  43   7  82  81  58
   PSTAT 170  INTRO MATH FINANCE 116  65  92  19 125  65  59  17  77  57  55
   PSTAT 171   MATH COMPOUND INT  73  77  96  47  84  68 102  32  64  69 108
  PSTAT 172A    ACTUARIAL STAT I  NA  49  NA  NA  NA  60  NA  NA  NA  43  NA
  PSTAT 172B   ACTUARIAL STAT II  14  NA  NA  NA  20  NA  NA  NA  23  NA  NA
   PSTAT 173         RISK THEORY  NA  NA  64  NA  NA  NA  35  NA  NA  NA  43
   PSTAT 174         TIME SERIES  NA  89  83  NA 104  63  NA  NA 170 118  69
   PSTAT 175   SURVIVAL ANALYSIS  71  NA  NA  NA  55  NA  18  NA  NA  NA  73
   PSTAT 176    ADV MATH FINANCE  17  NA  NA  NA  15  NA  NA  NA  13  NA  NA
   PSTAT 177      FINANCIAL RISK  31  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 182T  ACTUARIAL TUTORIAL  12  20  15  NA  17   6   4  NA   6   4   7
   PSTAT 183  ACTUARIAL CONCEPTS  28  NA  NA  NA  44  NA  NA  NA  46  NA  NA
   PSTAT 190        ULA TRAINING  NA  NA  14  NA  NA  NA   5  NA  NA  NA  20
   PSTAT 191       ULA PRACTICUM  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 193 INTERNSHIP IN STATS   4   3   4  28   6   4   8  20   6   3   2
   PSTAT 194  GRP STDY ADV STDNT  NA  NA  NA  11  29  NA  NA  NA  28  NA  NA
   PSTAT 195      SPECIAL TOPICS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 196   RESEARCH IN ACTSC  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 197A    DS CAPSTONE PREP  NA  NA  59  NA  NA  NA  58  NA  NA  NA  59
  PSTAT 197B DS CAPSTONE PROJECT  NA  58  NA  NA  NA  56  NA  NA  NA  53  NA
  PSTAT 197C DS CAPSTONE PROJECT  52  NA  NA  NA  53  NA  NA  NA  46  NA  NA
   PSTAT 199 INDEPENDENT STUDIES  23  22  18   6  19  17  23   6  21  17  21
 PSTAT 199RA INDEP RESEARCH ASST  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
 M22 S22 W22
 116 194 278
  NA  NA  NA
  63 294 284
  23  59  NA
  87 278 287
  NA  NA  NA
  NA  95  88
  NA  NA  93
  NA  NA  NA
  NA  NA  81
  65 244 229
 174 216 241
 109 119  NA
  NA 137 119
  NA  NA  NA
  67 250 123
  NA  78  91
 138 122  98
  NA  75  76
  NA  NA  NA
  22  NA  66
  NA  NA  NA
  NA  NA  NA
  51 130  77
  54 109  72
  41  74  69
  49  70  68
  NA  NA  60
  NA  26  NA
  NA  NA  50
  NA  61  74
  NA  NA  NA
  NA  15  NA
  NA  NA  NA
  NA  12   5
  NA  68  NA
  NA  NA  NA
  NA  NA  NA
  35   5   4
  NA  66  NA
  NA  NA  NA
  NA  NA  NA
  NA  NA  NA
  NA  NA  46
  NA  47  NA
  10  19   5
  NA  NA  NA

Another Dataset

Undergraduate PSTAT Course Enrollments

  • Observational Units: UCSB Courses

  • An observation: The enrollment for PSTAT 5A, titled “Understanding Data” was 167 in Spring 2025, 222 in Winter 2025, 213 in Fall 2024, etc.

  • Variables: Spring 2025, Winter 2025, Fall 2024, etc,

  • Is that right, though?

    • What is the value of Spring 2025 - is it really 167?
    • Isn’t 167 the value of a Course Enrollment variable?
    • Isn’t Spring 2025 actually itself a value of another variable (one we might call Quarter)?

Another Dataset

Undergraduate PSTAT Course Enrollments

  • At this point, we find ourselves at a bit of a crossroads.

  • For now, let’s adopt the following set of variables (tomorrow, we’ll discuss whether or not this choice is unique - spoiler alert, it is not!)

    • Course: the course ID
    • Course Title: the course title
    • Quarter: the quarter in which the course was offered
    • Enrollment: the enrollment count of the particular course in a particular quarter

Another Dataset

Undergraduate PSTAT Course Enrollments

      Course               Title S25 W25 F24 M24 S24 W24 F23 M23 S23 W23 F22
    PSTAT 5A  UNDERSTANDING DATA 167 222 213  76 258 283 549 110 212 279 499
    PSTAT 5H          STATISTICS  11  14  30  NA  31  24  25  NA  31  22   4
   PSTAT 5LS  STAT LIFE SCIENCES 355 340 348  59 304 299  NA  39 299 294  NA
     PSTAT 8  TRANS DS PROB STAT  70 105 137  22  83 134 132  18  86 156  70
    PSTAT 10  DATA SCIENCE PRINC 235 241 286  93 234 260 285  83 240 282 257
    PSTAT 99 INDEPENDENT STUDIES   1   2  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 100        DS_CONC&ANLS 109 131 108  NA  95  NA 104  48 125 127  NA
   PSTAT 105  INTRO N-PARAM METH  NA  79  NA  NA  NA  NA  39  NA  NA  NA  79
   PSTAT 109 STATISTICS FOR ECON  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 115 BAYES DATA ANALYSIS  81  56  74  25  74  96  16  15  38  70  63
  PSTAT 120A   PROB & STATISTICS 310 383 345  75 367 372 419  86 237 246 419
  PSTAT 120B   PROB & STATISTICS 312 329 236 136 382 241 261 102 256 256 165
  PSTAT 120C   PROB & STATISTICS 163  NA  37 129 131  39  19  81  65  31  87
   PSTAT 122 DESIGN OF EXPERMNTS 240 210 201  NA 177 162 167  NA 194 187 182
   PSTAT 123  SAMPLING TECHNIQUE  NA  NA  NA  NA  NA 137  NA  NA  NA  NA  NA
   PSTAT 126 REGRESSION ANALYSIS 197 214 272  94 147 200 123  84 149 175 182
   PSTAT 127    ADV STATS MODELS  NA  NA  72  NA  NA  NA  57  NA  NA  73  NA
   PSTAT 130    SAS BASE PROGRAM 116 120 121 108 122  97 120  95 119  98  97
   PSTAT 131  STAT MACHINE LEARN  96 156  64  80  93 138 150  55 108 197 178
   PSTAT 132 DATABASES FOR STATS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 134   STAT DATA SCIENCE  46  91  78  NA  70  78  80  NA  87  42  33
   PSTAT 135  BIG DATA ANALYTICS  96  NA  NA  NA  NA  99  NA  NA  NA  93  NA
   PSTAT 140 STATISTICAL PROCESS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 160A  STOCHASTIC PROCESS 132 217 126  NA 100 153 132  NA 108 161 184
  PSTAT 160B  STOCHASTIC PROCESS 116  77  86  NA 106  73  43   7  82  81  58
   PSTAT 170  INTRO MATH FINANCE 116  65  92  19 125  65  59  17  77  57  55
   PSTAT 171   MATH COMPOUND INT  73  77  96  47  84  68 102  32  64  69 108
  PSTAT 172A    ACTUARIAL STAT I  NA  49  NA  NA  NA  60  NA  NA  NA  43  NA
  PSTAT 172B   ACTUARIAL STAT II  14  NA  NA  NA  20  NA  NA  NA  23  NA  NA
   PSTAT 173         RISK THEORY  NA  NA  64  NA  NA  NA  35  NA  NA  NA  43
   PSTAT 174         TIME SERIES  NA  89  83  NA 104  63  NA  NA 170 118  69
   PSTAT 175   SURVIVAL ANALYSIS  71  NA  NA  NA  55  NA  18  NA  NA  NA  73
   PSTAT 176    ADV MATH FINANCE  17  NA  NA  NA  15  NA  NA  NA  13  NA  NA
   PSTAT 177      FINANCIAL RISK  31  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 182T  ACTUARIAL TUTORIAL  12  20  15  NA  17   6   4  NA   6   4   7
   PSTAT 183  ACTUARIAL CONCEPTS  28  NA  NA  NA  44  NA  NA  NA  46  NA  NA
   PSTAT 190        ULA TRAINING  NA  NA  14  NA  NA  NA   5  NA  NA  NA  20
   PSTAT 191       ULA PRACTICUM  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 193 INTERNSHIP IN STATS   4   3   4  28   6   4   8  20   6   3   2
   PSTAT 194  GRP STDY ADV STDNT  NA  NA  NA  11  29  NA  NA  NA  28  NA  NA
   PSTAT 195      SPECIAL TOPICS  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
   PSTAT 196   RESEARCH IN ACTSC  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  PSTAT 197A    DS CAPSTONE PREP  NA  NA  59  NA  NA  NA  58  NA  NA  NA  59
  PSTAT 197B DS CAPSTONE PROJECT  NA  58  NA  NA  NA  56  NA  NA  NA  53  NA
  PSTAT 197C DS CAPSTONE PROJECT  52  NA  NA  NA  53  NA  NA  NA  46  NA  NA
   PSTAT 199 INDEPENDENT STUDIES  23  22  18   6  19  17  23   6  21  17  21
 PSTAT 199RA INDEP RESEARCH ASST  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
 M22 S22 W22
 116 194 278
  NA  NA  NA
  63 294 284
  23  59  NA
  87 278 287
  NA  NA  NA
  NA  95  88
  NA  NA  93
  NA  NA  NA
  NA  NA  81
  65 244 229
 174 216 241
 109 119  NA
  NA 137 119
  NA  NA  NA
  67 250 123
  NA  78  91
 138 122  98
  NA  75  76
  NA  NA  NA
  22  NA  66
  NA  NA  NA
  NA  NA  NA
  51 130  77
  54 109  72
  41  74  69
  49  70  68
  NA  NA  60
  NA  26  NA
  NA  NA  50
  NA  61  74
  NA  NA  NA
  NA  15  NA
  NA  NA  NA
  NA  12   5
  NA  68  NA
  NA  NA  NA
  NA  NA  NA
  35   5   4
  NA  66  NA
  NA  NA  NA
  NA  NA  NA
  NA  NA  NA
  NA  NA  46
  NA  47  NA
  10  19   5
  NA  NA  NA
      Course               Title Quarter Enrollment
    PSTAT 5A  UNDERSTANDING DATA     S25        167
    PSTAT 5H          STATISTICS     S25         11
   PSTAT 5LS  STAT LIFE SCIENCES     S25        355
     PSTAT 8  TRANS DS PROB STAT     S25         70
    PSTAT 10  DATA SCIENCE PRINC     S25        235
    PSTAT 99 INDEPENDENT STUDIES     S25          1
   PSTAT 100        DS_CONC&ANLS     S25        109
   PSTAT 105  INTRO N-PARAM METH     S25         NA
   PSTAT 109 STATISTICS FOR ECON     S25         NA
   PSTAT 115 BAYES DATA ANALYSIS     S25         81
  PSTAT 120A   PROB & STATISTICS     S25        310
  PSTAT 120B   PROB & STATISTICS     S25        312
  PSTAT 120C   PROB & STATISTICS     S25        163
   PSTAT 122 DESIGN OF EXPERMNTS     S25        240
   PSTAT 123  SAMPLING TECHNIQUE     S25         NA
   PSTAT 126 REGRESSION ANALYSIS     S25        197
   PSTAT 127    ADV STATS MODELS     S25         NA
   PSTAT 130    SAS BASE PROGRAM     S25        116
   PSTAT 131  STAT MACHINE LEARN     S25         96
   PSTAT 132 DATABASES FOR STATS     S25         NA
   PSTAT 134   STAT DATA SCIENCE     S25         46
   PSTAT 135  BIG DATA ANALYTICS     S25         96
   PSTAT 140 STATISTICAL PROCESS     S25         NA
  PSTAT 160A  STOCHASTIC PROCESS     S25        132
  PSTAT 160B  STOCHASTIC PROCESS     S25        116
   PSTAT 170  INTRO MATH FINANCE     S25        116
   PSTAT 171   MATH COMPOUND INT     S25         73
  PSTAT 172A    ACTUARIAL STAT I     S25         NA
  PSTAT 172B   ACTUARIAL STAT II     S25         14
   PSTAT 173         RISK THEORY     S25         NA
   PSTAT 174         TIME SERIES     S25         NA
   PSTAT 175   SURVIVAL ANALYSIS     S25         71
   PSTAT 176    ADV MATH FINANCE     S25         17
   PSTAT 177      FINANCIAL RISK     S25         31
  PSTAT 182T  ACTUARIAL TUTORIAL     S25         12
   PSTAT 183  ACTUARIAL CONCEPTS     S25         28
   PSTAT 190        ULA TRAINING     S25         NA
   PSTAT 191       ULA PRACTICUM     S25         NA
   PSTAT 193 INTERNSHIP IN STATS     S25          4
   PSTAT 194  GRP STDY ADV STDNT     S25         NA
   PSTAT 195      SPECIAL TOPICS     S25         NA
   PSTAT 196   RESEARCH IN ACTSC     S25         NA
  PSTAT 197A    DS CAPSTONE PREP     S25         NA
  PSTAT 197B DS CAPSTONE PROJECT     S25         NA
  PSTAT 197C DS CAPSTONE PROJECT     S25         52
   PSTAT 199 INDEPENDENT STUDIES     S25         23
 PSTAT 199RA INDEP RESEARCH ASST     S25         NA
    PSTAT 5A  UNDERSTANDING DATA     W25        222
    PSTAT 5H          STATISTICS     W25         14
   PSTAT 5LS  STAT LIFE SCIENCES     W25        340
     PSTAT 8  TRANS DS PROB STAT     W25        105
    PSTAT 10  DATA SCIENCE PRINC     W25        241
    PSTAT 99 INDEPENDENT STUDIES     W25          2
   PSTAT 100        DS_CONC&ANLS     W25        131
   PSTAT 105  INTRO N-PARAM METH     W25         79
   PSTAT 109 STATISTICS FOR ECON     W25         NA
   PSTAT 115 BAYES DATA ANALYSIS     W25         56
  PSTAT 120A   PROB & STATISTICS     W25        383
  PSTAT 120B   PROB & STATISTICS     W25        329
  PSTAT 120C   PROB & STATISTICS     W25         NA
   PSTAT 122 DESIGN OF EXPERMNTS     W25        210
   PSTAT 123  SAMPLING TECHNIQUE     W25         NA
   PSTAT 126 REGRESSION ANALYSIS     W25        214
   PSTAT 127    ADV STATS MODELS     W25         NA
   PSTAT 130    SAS BASE PROGRAM     W25        120
   PSTAT 131  STAT MACHINE LEARN     W25        156
   PSTAT 132 DATABASES FOR STATS     W25         NA
   PSTAT 134   STAT DATA SCIENCE     W25         91
   PSTAT 135  BIG DATA ANALYTICS     W25         NA
   PSTAT 140 STATISTICAL PROCESS     W25         NA
  PSTAT 160A  STOCHASTIC PROCESS     W25        217
  PSTAT 160B  STOCHASTIC PROCESS     W25         77
   PSTAT 170  INTRO MATH FINANCE     W25         65
   PSTAT 171   MATH COMPOUND INT     W25         77
  PSTAT 172A    ACTUARIAL STAT I     W25         49
  PSTAT 172B   ACTUARIAL STAT II     W25         NA
   PSTAT 173         RISK THEORY     W25         NA
   PSTAT 174         TIME SERIES     W25         89
   PSTAT 175   SURVIVAL ANALYSIS     W25         NA
   PSTAT 176    ADV MATH FINANCE     W25         NA
   PSTAT 177      FINANCIAL RISK     W25         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     W25         20
   PSTAT 183  ACTUARIAL CONCEPTS     W25         NA
   PSTAT 190        ULA TRAINING     W25         NA
   PSTAT 191       ULA PRACTICUM     W25         NA
   PSTAT 193 INTERNSHIP IN STATS     W25          3
   PSTAT 194  GRP STDY ADV STDNT     W25         NA
   PSTAT 195      SPECIAL TOPICS     W25         NA
   PSTAT 196   RESEARCH IN ACTSC     W25         NA
  PSTAT 197A    DS CAPSTONE PREP     W25         NA
  PSTAT 197B DS CAPSTONE PROJECT     W25         58
  PSTAT 197C DS CAPSTONE PROJECT     W25         NA
   PSTAT 199 INDEPENDENT STUDIES     W25         22
 PSTAT 199RA INDEP RESEARCH ASST     W25         NA
    PSTAT 5A  UNDERSTANDING DATA     F24        213
    PSTAT 5H          STATISTICS     F24         30
   PSTAT 5LS  STAT LIFE SCIENCES     F24        348
     PSTAT 8  TRANS DS PROB STAT     F24        137
    PSTAT 10  DATA SCIENCE PRINC     F24        286
    PSTAT 99 INDEPENDENT STUDIES     F24         NA
   PSTAT 100        DS_CONC&ANLS     F24        108
   PSTAT 105  INTRO N-PARAM METH     F24         NA
   PSTAT 109 STATISTICS FOR ECON     F24         NA
   PSTAT 115 BAYES DATA ANALYSIS     F24         74
  PSTAT 120A   PROB & STATISTICS     F24        345
  PSTAT 120B   PROB & STATISTICS     F24        236
  PSTAT 120C   PROB & STATISTICS     F24         37
   PSTAT 122 DESIGN OF EXPERMNTS     F24        201
   PSTAT 123  SAMPLING TECHNIQUE     F24         NA
   PSTAT 126 REGRESSION ANALYSIS     F24        272
   PSTAT 127    ADV STATS MODELS     F24         72
   PSTAT 130    SAS BASE PROGRAM     F24        121
   PSTAT 131  STAT MACHINE LEARN     F24         64
   PSTAT 132 DATABASES FOR STATS     F24         NA
   PSTAT 134   STAT DATA SCIENCE     F24         78
   PSTAT 135  BIG DATA ANALYTICS     F24         NA
   PSTAT 140 STATISTICAL PROCESS     F24         NA
  PSTAT 160A  STOCHASTIC PROCESS     F24        126
  PSTAT 160B  STOCHASTIC PROCESS     F24         86
   PSTAT 170  INTRO MATH FINANCE     F24         92
   PSTAT 171   MATH COMPOUND INT     F24         96
  PSTAT 172A    ACTUARIAL STAT I     F24         NA
  PSTAT 172B   ACTUARIAL STAT II     F24         NA
   PSTAT 173         RISK THEORY     F24         64
   PSTAT 174         TIME SERIES     F24         83
   PSTAT 175   SURVIVAL ANALYSIS     F24         NA
   PSTAT 176    ADV MATH FINANCE     F24         NA
   PSTAT 177      FINANCIAL RISK     F24         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     F24         15
   PSTAT 183  ACTUARIAL CONCEPTS     F24         NA
   PSTAT 190        ULA TRAINING     F24         14
   PSTAT 191       ULA PRACTICUM     F24         NA
   PSTAT 193 INTERNSHIP IN STATS     F24          4
   PSTAT 194  GRP STDY ADV STDNT     F24         NA
   PSTAT 195      SPECIAL TOPICS     F24         NA
   PSTAT 196   RESEARCH IN ACTSC     F24         NA
  PSTAT 197A    DS CAPSTONE PREP     F24         59
  PSTAT 197B DS CAPSTONE PROJECT     F24         NA
  PSTAT 197C DS CAPSTONE PROJECT     F24         NA
   PSTAT 199 INDEPENDENT STUDIES     F24         18
 PSTAT 199RA INDEP RESEARCH ASST     F24         NA
    PSTAT 5A  UNDERSTANDING DATA     M24         76
    PSTAT 5H          STATISTICS     M24         NA
   PSTAT 5LS  STAT LIFE SCIENCES     M24         59
     PSTAT 8  TRANS DS PROB STAT     M24         22
    PSTAT 10  DATA SCIENCE PRINC     M24         93
    PSTAT 99 INDEPENDENT STUDIES     M24         NA
   PSTAT 100        DS_CONC&ANLS     M24         NA
   PSTAT 105  INTRO N-PARAM METH     M24         NA
   PSTAT 109 STATISTICS FOR ECON     M24         NA
   PSTAT 115 BAYES DATA ANALYSIS     M24         25
  PSTAT 120A   PROB & STATISTICS     M24         75
  PSTAT 120B   PROB & STATISTICS     M24        136
  PSTAT 120C   PROB & STATISTICS     M24        129
   PSTAT 122 DESIGN OF EXPERMNTS     M24         NA
   PSTAT 123  SAMPLING TECHNIQUE     M24         NA
   PSTAT 126 REGRESSION ANALYSIS     M24         94
   PSTAT 127    ADV STATS MODELS     M24         NA
   PSTAT 130    SAS BASE PROGRAM     M24        108
   PSTAT 131  STAT MACHINE LEARN     M24         80
   PSTAT 132 DATABASES FOR STATS     M24         NA
   PSTAT 134   STAT DATA SCIENCE     M24         NA
   PSTAT 135  BIG DATA ANALYTICS     M24         NA
   PSTAT 140 STATISTICAL PROCESS     M24         NA
  PSTAT 160A  STOCHASTIC PROCESS     M24         NA
  PSTAT 160B  STOCHASTIC PROCESS     M24         NA
   PSTAT 170  INTRO MATH FINANCE     M24         19
   PSTAT 171   MATH COMPOUND INT     M24         47
  PSTAT 172A    ACTUARIAL STAT I     M24         NA
  PSTAT 172B   ACTUARIAL STAT II     M24         NA
   PSTAT 173         RISK THEORY     M24         NA
   PSTAT 174         TIME SERIES     M24         NA
   PSTAT 175   SURVIVAL ANALYSIS     M24         NA
   PSTAT 176    ADV MATH FINANCE     M24         NA
   PSTAT 177      FINANCIAL RISK     M24         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     M24         NA
   PSTAT 183  ACTUARIAL CONCEPTS     M24         NA
   PSTAT 190        ULA TRAINING     M24         NA
   PSTAT 191       ULA PRACTICUM     M24         NA
   PSTAT 193 INTERNSHIP IN STATS     M24         28
   PSTAT 194  GRP STDY ADV STDNT     M24         11
   PSTAT 195      SPECIAL TOPICS     M24         NA
   PSTAT 196   RESEARCH IN ACTSC     M24         NA
  PSTAT 197A    DS CAPSTONE PREP     M24         NA
  PSTAT 197B DS CAPSTONE PROJECT     M24         NA
  PSTAT 197C DS CAPSTONE PROJECT     M24         NA
   PSTAT 199 INDEPENDENT STUDIES     M24          6
 PSTAT 199RA INDEP RESEARCH ASST     M24         NA
    PSTAT 5A  UNDERSTANDING DATA     S24        258
    PSTAT 5H          STATISTICS     S24         31
   PSTAT 5LS  STAT LIFE SCIENCES     S24        304
     PSTAT 8  TRANS DS PROB STAT     S24         83
    PSTAT 10  DATA SCIENCE PRINC     S24        234
    PSTAT 99 INDEPENDENT STUDIES     S24         NA
   PSTAT 100        DS_CONC&ANLS     S24         95
   PSTAT 105  INTRO N-PARAM METH     S24         NA
   PSTAT 109 STATISTICS FOR ECON     S24         NA
   PSTAT 115 BAYES DATA ANALYSIS     S24         74
  PSTAT 120A   PROB & STATISTICS     S24        367
  PSTAT 120B   PROB & STATISTICS     S24        382
  PSTAT 120C   PROB & STATISTICS     S24        131
   PSTAT 122 DESIGN OF EXPERMNTS     S24        177
   PSTAT 123  SAMPLING TECHNIQUE     S24         NA
   PSTAT 126 REGRESSION ANALYSIS     S24        147
   PSTAT 127    ADV STATS MODELS     S24         NA
   PSTAT 130    SAS BASE PROGRAM     S24        122
   PSTAT 131  STAT MACHINE LEARN     S24         93
   PSTAT 132 DATABASES FOR STATS     S24         NA
   PSTAT 134   STAT DATA SCIENCE     S24         70
   PSTAT 135  BIG DATA ANALYTICS     S24         NA
   PSTAT 140 STATISTICAL PROCESS     S24         NA
  PSTAT 160A  STOCHASTIC PROCESS     S24        100
  PSTAT 160B  STOCHASTIC PROCESS     S24        106
   PSTAT 170  INTRO MATH FINANCE     S24        125
   PSTAT 171   MATH COMPOUND INT     S24         84
  PSTAT 172A    ACTUARIAL STAT I     S24         NA
  PSTAT 172B   ACTUARIAL STAT II     S24         20
   PSTAT 173         RISK THEORY     S24         NA
   PSTAT 174         TIME SERIES     S24        104
   PSTAT 175   SURVIVAL ANALYSIS     S24         55
   PSTAT 176    ADV MATH FINANCE     S24         15
   PSTAT 177      FINANCIAL RISK     S24         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     S24         17
   PSTAT 183  ACTUARIAL CONCEPTS     S24         44
   PSTAT 190        ULA TRAINING     S24         NA
   PSTAT 191       ULA PRACTICUM     S24         NA
   PSTAT 193 INTERNSHIP IN STATS     S24          6
   PSTAT 194  GRP STDY ADV STDNT     S24         29
   PSTAT 195      SPECIAL TOPICS     S24         NA
   PSTAT 196   RESEARCH IN ACTSC     S24         NA
  PSTAT 197A    DS CAPSTONE PREP     S24         NA
  PSTAT 197B DS CAPSTONE PROJECT     S24         NA
  PSTAT 197C DS CAPSTONE PROJECT     S24         53
   PSTAT 199 INDEPENDENT STUDIES     S24         19
 PSTAT 199RA INDEP RESEARCH ASST     S24         NA
    PSTAT 5A  UNDERSTANDING DATA     W24        283
    PSTAT 5H          STATISTICS     W24         24
   PSTAT 5LS  STAT LIFE SCIENCES     W24        299
     PSTAT 8  TRANS DS PROB STAT     W24        134
    PSTAT 10  DATA SCIENCE PRINC     W24        260
    PSTAT 99 INDEPENDENT STUDIES     W24         NA
   PSTAT 100        DS_CONC&ANLS     W24         NA
   PSTAT 105  INTRO N-PARAM METH     W24         NA
   PSTAT 109 STATISTICS FOR ECON     W24         NA
   PSTAT 115 BAYES DATA ANALYSIS     W24         96
  PSTAT 120A   PROB & STATISTICS     W24        372
  PSTAT 120B   PROB & STATISTICS     W24        241
  PSTAT 120C   PROB & STATISTICS     W24         39
   PSTAT 122 DESIGN OF EXPERMNTS     W24        162
   PSTAT 123  SAMPLING TECHNIQUE     W24        137
   PSTAT 126 REGRESSION ANALYSIS     W24        200
   PSTAT 127    ADV STATS MODELS     W24         NA
   PSTAT 130    SAS BASE PROGRAM     W24         97
   PSTAT 131  STAT MACHINE LEARN     W24        138
   PSTAT 132 DATABASES FOR STATS     W24         NA
   PSTAT 134   STAT DATA SCIENCE     W24         78
   PSTAT 135  BIG DATA ANALYTICS     W24         99
   PSTAT 140 STATISTICAL PROCESS     W24         NA
  PSTAT 160A  STOCHASTIC PROCESS     W24        153
  PSTAT 160B  STOCHASTIC PROCESS     W24         73
   PSTAT 170  INTRO MATH FINANCE     W24         65
   PSTAT 171   MATH COMPOUND INT     W24         68
  PSTAT 172A    ACTUARIAL STAT I     W24         60
  PSTAT 172B   ACTUARIAL STAT II     W24         NA
   PSTAT 173         RISK THEORY     W24         NA
   PSTAT 174         TIME SERIES     W24         63
   PSTAT 175   SURVIVAL ANALYSIS     W24         NA
   PSTAT 176    ADV MATH FINANCE     W24         NA
   PSTAT 177      FINANCIAL RISK     W24         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     W24          6
   PSTAT 183  ACTUARIAL CONCEPTS     W24         NA
   PSTAT 190        ULA TRAINING     W24         NA
   PSTAT 191       ULA PRACTICUM     W24         NA
   PSTAT 193 INTERNSHIP IN STATS     W24          4
   PSTAT 194  GRP STDY ADV STDNT     W24         NA
   PSTAT 195      SPECIAL TOPICS     W24         NA
   PSTAT 196   RESEARCH IN ACTSC     W24         NA
  PSTAT 197A    DS CAPSTONE PREP     W24         NA
  PSTAT 197B DS CAPSTONE PROJECT     W24         56
  PSTAT 197C DS CAPSTONE PROJECT     W24         NA
   PSTAT 199 INDEPENDENT STUDIES     W24         17
 PSTAT 199RA INDEP RESEARCH ASST     W24         NA
    PSTAT 5A  UNDERSTANDING DATA     F23        549
    PSTAT 5H          STATISTICS     F23         25
   PSTAT 5LS  STAT LIFE SCIENCES     F23         NA
     PSTAT 8  TRANS DS PROB STAT     F23        132
    PSTAT 10  DATA SCIENCE PRINC     F23        285
    PSTAT 99 INDEPENDENT STUDIES     F23         NA
   PSTAT 100        DS_CONC&ANLS     F23        104
   PSTAT 105  INTRO N-PARAM METH     F23         39
   PSTAT 109 STATISTICS FOR ECON     F23         NA
   PSTAT 115 BAYES DATA ANALYSIS     F23         16
  PSTAT 120A   PROB & STATISTICS     F23        419
  PSTAT 120B   PROB & STATISTICS     F23        261
  PSTAT 120C   PROB & STATISTICS     F23         19
   PSTAT 122 DESIGN OF EXPERMNTS     F23        167
   PSTAT 123  SAMPLING TECHNIQUE     F23         NA
   PSTAT 126 REGRESSION ANALYSIS     F23        123
   PSTAT 127    ADV STATS MODELS     F23         57
   PSTAT 130    SAS BASE PROGRAM     F23        120
   PSTAT 131  STAT MACHINE LEARN     F23        150
   PSTAT 132 DATABASES FOR STATS     F23         NA
   PSTAT 134   STAT DATA SCIENCE     F23         80
   PSTAT 135  BIG DATA ANALYTICS     F23         NA
   PSTAT 140 STATISTICAL PROCESS     F23         NA
  PSTAT 160A  STOCHASTIC PROCESS     F23        132
  PSTAT 160B  STOCHASTIC PROCESS     F23         43
   PSTAT 170  INTRO MATH FINANCE     F23         59
   PSTAT 171   MATH COMPOUND INT     F23        102
  PSTAT 172A    ACTUARIAL STAT I     F23         NA
  PSTAT 172B   ACTUARIAL STAT II     F23         NA
   PSTAT 173         RISK THEORY     F23         35
   PSTAT 174         TIME SERIES     F23         NA
   PSTAT 175   SURVIVAL ANALYSIS     F23         18
   PSTAT 176    ADV MATH FINANCE     F23         NA
   PSTAT 177      FINANCIAL RISK     F23         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     F23          4
   PSTAT 183  ACTUARIAL CONCEPTS     F23         NA
   PSTAT 190        ULA TRAINING     F23          5
   PSTAT 191       ULA PRACTICUM     F23         NA
   PSTAT 193 INTERNSHIP IN STATS     F23          8
   PSTAT 194  GRP STDY ADV STDNT     F23         NA
   PSTAT 195      SPECIAL TOPICS     F23         NA
   PSTAT 196   RESEARCH IN ACTSC     F23         NA
  PSTAT 197A    DS CAPSTONE PREP     F23         58
  PSTAT 197B DS CAPSTONE PROJECT     F23         NA
  PSTAT 197C DS CAPSTONE PROJECT     F23         NA
   PSTAT 199 INDEPENDENT STUDIES     F23         23
 PSTAT 199RA INDEP RESEARCH ASST     F23         NA
    PSTAT 5A  UNDERSTANDING DATA     M23        110
    PSTAT 5H          STATISTICS     M23         NA
   PSTAT 5LS  STAT LIFE SCIENCES     M23         39
     PSTAT 8  TRANS DS PROB STAT     M23         18
    PSTAT 10  DATA SCIENCE PRINC     M23         83
    PSTAT 99 INDEPENDENT STUDIES     M23         NA
   PSTAT 100        DS_CONC&ANLS     M23         48
   PSTAT 105  INTRO N-PARAM METH     M23         NA
   PSTAT 109 STATISTICS FOR ECON     M23         NA
   PSTAT 115 BAYES DATA ANALYSIS     M23         15
  PSTAT 120A   PROB & STATISTICS     M23         86
  PSTAT 120B   PROB & STATISTICS     M23        102
  PSTAT 120C   PROB & STATISTICS     M23         81
   PSTAT 122 DESIGN OF EXPERMNTS     M23         NA
   PSTAT 123  SAMPLING TECHNIQUE     M23         NA
   PSTAT 126 REGRESSION ANALYSIS     M23         84
   PSTAT 127    ADV STATS MODELS     M23         NA
   PSTAT 130    SAS BASE PROGRAM     M23         95
   PSTAT 131  STAT MACHINE LEARN     M23         55
   PSTAT 132 DATABASES FOR STATS     M23         NA
   PSTAT 134   STAT DATA SCIENCE     M23         NA
   PSTAT 135  BIG DATA ANALYTICS     M23         NA
   PSTAT 140 STATISTICAL PROCESS     M23         NA
  PSTAT 160A  STOCHASTIC PROCESS     M23         NA
  PSTAT 160B  STOCHASTIC PROCESS     M23          7
   PSTAT 170  INTRO MATH FINANCE     M23         17
   PSTAT 171   MATH COMPOUND INT     M23         32
  PSTAT 172A    ACTUARIAL STAT I     M23         NA
  PSTAT 172B   ACTUARIAL STAT II     M23         NA
   PSTAT 173         RISK THEORY     M23         NA
   PSTAT 174         TIME SERIES     M23         NA
   PSTAT 175   SURVIVAL ANALYSIS     M23         NA
   PSTAT 176    ADV MATH FINANCE     M23         NA
   PSTAT 177      FINANCIAL RISK     M23         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     M23         NA
   PSTAT 183  ACTUARIAL CONCEPTS     M23         NA
   PSTAT 190        ULA TRAINING     M23         NA
   PSTAT 191       ULA PRACTICUM     M23         NA
   PSTAT 193 INTERNSHIP IN STATS     M23         20
   PSTAT 194  GRP STDY ADV STDNT     M23         NA
   PSTAT 195      SPECIAL TOPICS     M23         NA
   PSTAT 196   RESEARCH IN ACTSC     M23         NA
  PSTAT 197A    DS CAPSTONE PREP     M23         NA
  PSTAT 197B DS CAPSTONE PROJECT     M23         NA
  PSTAT 197C DS CAPSTONE PROJECT     M23         NA
   PSTAT 199 INDEPENDENT STUDIES     M23          6
 PSTAT 199RA INDEP RESEARCH ASST     M23         NA
    PSTAT 5A  UNDERSTANDING DATA     S23        212
    PSTAT 5H          STATISTICS     S23         31
   PSTAT 5LS  STAT LIFE SCIENCES     S23        299
     PSTAT 8  TRANS DS PROB STAT     S23         86
    PSTAT 10  DATA SCIENCE PRINC     S23        240
    PSTAT 99 INDEPENDENT STUDIES     S23         NA
   PSTAT 100        DS_CONC&ANLS     S23        125
   PSTAT 105  INTRO N-PARAM METH     S23         NA
   PSTAT 109 STATISTICS FOR ECON     S23         NA
   PSTAT 115 BAYES DATA ANALYSIS     S23         38
  PSTAT 120A   PROB & STATISTICS     S23        237
  PSTAT 120B   PROB & STATISTICS     S23        256
  PSTAT 120C   PROB & STATISTICS     S23         65
   PSTAT 122 DESIGN OF EXPERMNTS     S23        194
   PSTAT 123  SAMPLING TECHNIQUE     S23         NA
   PSTAT 126 REGRESSION ANALYSIS     S23        149
   PSTAT 127    ADV STATS MODELS     S23         NA
   PSTAT 130    SAS BASE PROGRAM     S23        119
   PSTAT 131  STAT MACHINE LEARN     S23        108
   PSTAT 132 DATABASES FOR STATS     S23         NA
   PSTAT 134   STAT DATA SCIENCE     S23         87
   PSTAT 135  BIG DATA ANALYTICS     S23         NA
   PSTAT 140 STATISTICAL PROCESS     S23         NA
  PSTAT 160A  STOCHASTIC PROCESS     S23        108
  PSTAT 160B  STOCHASTIC PROCESS     S23         82
   PSTAT 170  INTRO MATH FINANCE     S23         77
   PSTAT 171   MATH COMPOUND INT     S23         64
  PSTAT 172A    ACTUARIAL STAT I     S23         NA
  PSTAT 172B   ACTUARIAL STAT II     S23         23
   PSTAT 173         RISK THEORY     S23         NA
   PSTAT 174         TIME SERIES     S23        170
   PSTAT 175   SURVIVAL ANALYSIS     S23         NA
   PSTAT 176    ADV MATH FINANCE     S23         13
   PSTAT 177      FINANCIAL RISK     S23         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     S23          6
   PSTAT 183  ACTUARIAL CONCEPTS     S23         46
   PSTAT 190        ULA TRAINING     S23         NA
   PSTAT 191       ULA PRACTICUM     S23         NA
   PSTAT 193 INTERNSHIP IN STATS     S23          6
   PSTAT 194  GRP STDY ADV STDNT     S23         28
   PSTAT 195      SPECIAL TOPICS     S23         NA
   PSTAT 196   RESEARCH IN ACTSC     S23         NA
  PSTAT 197A    DS CAPSTONE PREP     S23         NA
  PSTAT 197B DS CAPSTONE PROJECT     S23         NA
  PSTAT 197C DS CAPSTONE PROJECT     S23         46
   PSTAT 199 INDEPENDENT STUDIES     S23         21
 PSTAT 199RA INDEP RESEARCH ASST     S23         NA
    PSTAT 5A  UNDERSTANDING DATA     W23        279
    PSTAT 5H          STATISTICS     W23         22
   PSTAT 5LS  STAT LIFE SCIENCES     W23        294
     PSTAT 8  TRANS DS PROB STAT     W23        156
    PSTAT 10  DATA SCIENCE PRINC     W23        282
    PSTAT 99 INDEPENDENT STUDIES     W23         NA
   PSTAT 100        DS_CONC&ANLS     W23        127
   PSTAT 105  INTRO N-PARAM METH     W23         NA
   PSTAT 109 STATISTICS FOR ECON     W23         NA
   PSTAT 115 BAYES DATA ANALYSIS     W23         70
  PSTAT 120A   PROB & STATISTICS     W23        246
  PSTAT 120B   PROB & STATISTICS     W23        256
  PSTAT 120C   PROB & STATISTICS     W23         31
   PSTAT 122 DESIGN OF EXPERMNTS     W23        187
   PSTAT 123  SAMPLING TECHNIQUE     W23         NA
   PSTAT 126 REGRESSION ANALYSIS     W23        175
   PSTAT 127    ADV STATS MODELS     W23         73
   PSTAT 130    SAS BASE PROGRAM     W23         98
   PSTAT 131  STAT MACHINE LEARN     W23        197
   PSTAT 132 DATABASES FOR STATS     W23         NA
   PSTAT 134   STAT DATA SCIENCE     W23         42
   PSTAT 135  BIG DATA ANALYTICS     W23         93
   PSTAT 140 STATISTICAL PROCESS     W23         NA
  PSTAT 160A  STOCHASTIC PROCESS     W23        161
  PSTAT 160B  STOCHASTIC PROCESS     W23         81
   PSTAT 170  INTRO MATH FINANCE     W23         57
   PSTAT 171   MATH COMPOUND INT     W23         69
  PSTAT 172A    ACTUARIAL STAT I     W23         43
  PSTAT 172B   ACTUARIAL STAT II     W23         NA
   PSTAT 173         RISK THEORY     W23         NA
   PSTAT 174         TIME SERIES     W23        118
   PSTAT 175   SURVIVAL ANALYSIS     W23         NA
   PSTAT 176    ADV MATH FINANCE     W23         NA
   PSTAT 177      FINANCIAL RISK     W23         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     W23          4
   PSTAT 183  ACTUARIAL CONCEPTS     W23         NA
   PSTAT 190        ULA TRAINING     W23         NA
   PSTAT 191       ULA PRACTICUM     W23         NA
   PSTAT 193 INTERNSHIP IN STATS     W23          3
   PSTAT 194  GRP STDY ADV STDNT     W23         NA
   PSTAT 195      SPECIAL TOPICS     W23         NA
   PSTAT 196   RESEARCH IN ACTSC     W23         NA
  PSTAT 197A    DS CAPSTONE PREP     W23         NA
  PSTAT 197B DS CAPSTONE PROJECT     W23         53
  PSTAT 197C DS CAPSTONE PROJECT     W23         NA
   PSTAT 199 INDEPENDENT STUDIES     W23         17
 PSTAT 199RA INDEP RESEARCH ASST     W23         NA
    PSTAT 5A  UNDERSTANDING DATA     F22        499
    PSTAT 5H          STATISTICS     F22          4
   PSTAT 5LS  STAT LIFE SCIENCES     F22         NA
     PSTAT 8  TRANS DS PROB STAT     F22         70
    PSTAT 10  DATA SCIENCE PRINC     F22        257
    PSTAT 99 INDEPENDENT STUDIES     F22         NA
   PSTAT 100        DS_CONC&ANLS     F22         NA
   PSTAT 105  INTRO N-PARAM METH     F22         79
   PSTAT 109 STATISTICS FOR ECON     F22         NA
   PSTAT 115 BAYES DATA ANALYSIS     F22         63
  PSTAT 120A   PROB & STATISTICS     F22        419
  PSTAT 120B   PROB & STATISTICS     F22        165
  PSTAT 120C   PROB & STATISTICS     F22         87
   PSTAT 122 DESIGN OF EXPERMNTS     F22        182
   PSTAT 123  SAMPLING TECHNIQUE     F22         NA
   PSTAT 126 REGRESSION ANALYSIS     F22        182
   PSTAT 127    ADV STATS MODELS     F22         NA
   PSTAT 130    SAS BASE PROGRAM     F22         97
   PSTAT 131  STAT MACHINE LEARN     F22        178
   PSTAT 132 DATABASES FOR STATS     F22         NA
   PSTAT 134   STAT DATA SCIENCE     F22         33
   PSTAT 135  BIG DATA ANALYTICS     F22         NA
   PSTAT 140 STATISTICAL PROCESS     F22         NA
  PSTAT 160A  STOCHASTIC PROCESS     F22        184
  PSTAT 160B  STOCHASTIC PROCESS     F22         58
   PSTAT 170  INTRO MATH FINANCE     F22         55
   PSTAT 171   MATH COMPOUND INT     F22        108
  PSTAT 172A    ACTUARIAL STAT I     F22         NA
  PSTAT 172B   ACTUARIAL STAT II     F22         NA
   PSTAT 173         RISK THEORY     F22         43
   PSTAT 174         TIME SERIES     F22         69
   PSTAT 175   SURVIVAL ANALYSIS     F22         73
   PSTAT 176    ADV MATH FINANCE     F22         NA
   PSTAT 177      FINANCIAL RISK     F22         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     F22          7
   PSTAT 183  ACTUARIAL CONCEPTS     F22         NA
   PSTAT 190        ULA TRAINING     F22         20
   PSTAT 191       ULA PRACTICUM     F22         NA
   PSTAT 193 INTERNSHIP IN STATS     F22          2
   PSTAT 194  GRP STDY ADV STDNT     F22         NA
   PSTAT 195      SPECIAL TOPICS     F22         NA
   PSTAT 196   RESEARCH IN ACTSC     F22         NA
  PSTAT 197A    DS CAPSTONE PREP     F22         59
  PSTAT 197B DS CAPSTONE PROJECT     F22         NA
  PSTAT 197C DS CAPSTONE PROJECT     F22         NA
   PSTAT 199 INDEPENDENT STUDIES     F22         21
 PSTAT 199RA INDEP RESEARCH ASST     F22         NA
    PSTAT 5A  UNDERSTANDING DATA     M22        116
    PSTAT 5H          STATISTICS     M22         NA
   PSTAT 5LS  STAT LIFE SCIENCES     M22         63
     PSTAT 8  TRANS DS PROB STAT     M22         23
    PSTAT 10  DATA SCIENCE PRINC     M22         87
    PSTAT 99 INDEPENDENT STUDIES     M22         NA
   PSTAT 100        DS_CONC&ANLS     M22         NA
   PSTAT 105  INTRO N-PARAM METH     M22         NA
   PSTAT 109 STATISTICS FOR ECON     M22         NA
   PSTAT 115 BAYES DATA ANALYSIS     M22         NA
  PSTAT 120A   PROB & STATISTICS     M22         65
  PSTAT 120B   PROB & STATISTICS     M22        174
  PSTAT 120C   PROB & STATISTICS     M22        109
   PSTAT 122 DESIGN OF EXPERMNTS     M22         NA
   PSTAT 123  SAMPLING TECHNIQUE     M22         NA
   PSTAT 126 REGRESSION ANALYSIS     M22         67
   PSTAT 127    ADV STATS MODELS     M22         NA
   PSTAT 130    SAS BASE PROGRAM     M22        138
   PSTAT 131  STAT MACHINE LEARN     M22         NA
   PSTAT 132 DATABASES FOR STATS     M22         NA
   PSTAT 134   STAT DATA SCIENCE     M22         22
   PSTAT 135  BIG DATA ANALYTICS     M22         NA
   PSTAT 140 STATISTICAL PROCESS     M22         NA
  PSTAT 160A  STOCHASTIC PROCESS     M22         51
  PSTAT 160B  STOCHASTIC PROCESS     M22         54
   PSTAT 170  INTRO MATH FINANCE     M22         41
   PSTAT 171   MATH COMPOUND INT     M22         49
  PSTAT 172A    ACTUARIAL STAT I     M22         NA
  PSTAT 172B   ACTUARIAL STAT II     M22         NA
   PSTAT 173         RISK THEORY     M22         NA
   PSTAT 174         TIME SERIES     M22         NA
   PSTAT 175   SURVIVAL ANALYSIS     M22         NA
   PSTAT 176    ADV MATH FINANCE     M22         NA
   PSTAT 177      FINANCIAL RISK     M22         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     M22         NA
   PSTAT 183  ACTUARIAL CONCEPTS     M22         NA
   PSTAT 190        ULA TRAINING     M22         NA
   PSTAT 191       ULA PRACTICUM     M22         NA
   PSTAT 193 INTERNSHIP IN STATS     M22         35
   PSTAT 194  GRP STDY ADV STDNT     M22         NA
   PSTAT 195      SPECIAL TOPICS     M22         NA
   PSTAT 196   RESEARCH IN ACTSC     M22         NA
  PSTAT 197A    DS CAPSTONE PREP     M22         NA
  PSTAT 197B DS CAPSTONE PROJECT     M22         NA
  PSTAT 197C DS CAPSTONE PROJECT     M22         NA
   PSTAT 199 INDEPENDENT STUDIES     M22         10
 PSTAT 199RA INDEP RESEARCH ASST     M22         NA
    PSTAT 5A  UNDERSTANDING DATA     S22        194
    PSTAT 5H          STATISTICS     S22         NA
   PSTAT 5LS  STAT LIFE SCIENCES     S22        294
     PSTAT 8  TRANS DS PROB STAT     S22         59
    PSTAT 10  DATA SCIENCE PRINC     S22        278
    PSTAT 99 INDEPENDENT STUDIES     S22         NA
   PSTAT 100        DS_CONC&ANLS     S22         95
   PSTAT 105  INTRO N-PARAM METH     S22         NA
   PSTAT 109 STATISTICS FOR ECON     S22         NA
   PSTAT 115 BAYES DATA ANALYSIS     S22         NA
  PSTAT 120A   PROB & STATISTICS     S22        244
  PSTAT 120B   PROB & STATISTICS     S22        216
  PSTAT 120C   PROB & STATISTICS     S22        119
   PSTAT 122 DESIGN OF EXPERMNTS     S22        137
   PSTAT 123  SAMPLING TECHNIQUE     S22         NA
   PSTAT 126 REGRESSION ANALYSIS     S22        250
   PSTAT 127    ADV STATS MODELS     S22         78
   PSTAT 130    SAS BASE PROGRAM     S22        122
   PSTAT 131  STAT MACHINE LEARN     S22         75
   PSTAT 132 DATABASES FOR STATS     S22         NA
   PSTAT 134   STAT DATA SCIENCE     S22         NA
   PSTAT 135  BIG DATA ANALYTICS     S22         NA
   PSTAT 140 STATISTICAL PROCESS     S22         NA
  PSTAT 160A  STOCHASTIC PROCESS     S22        130
  PSTAT 160B  STOCHASTIC PROCESS     S22        109
   PSTAT 170  INTRO MATH FINANCE     S22         74
   PSTAT 171   MATH COMPOUND INT     S22         70
  PSTAT 172A    ACTUARIAL STAT I     S22         NA
  PSTAT 172B   ACTUARIAL STAT II     S22         26
   PSTAT 173         RISK THEORY     S22         NA
   PSTAT 174         TIME SERIES     S22         61
   PSTAT 175   SURVIVAL ANALYSIS     S22         NA
   PSTAT 176    ADV MATH FINANCE     S22         15
   PSTAT 177      FINANCIAL RISK     S22         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     S22         12
   PSTAT 183  ACTUARIAL CONCEPTS     S22         68
   PSTAT 190        ULA TRAINING     S22         NA
   PSTAT 191       ULA PRACTICUM     S22         NA
   PSTAT 193 INTERNSHIP IN STATS     S22          5
   PSTAT 194  GRP STDY ADV STDNT     S22         66
   PSTAT 195      SPECIAL TOPICS     S22         NA
   PSTAT 196   RESEARCH IN ACTSC     S22         NA
  PSTAT 197A    DS CAPSTONE PREP     S22         NA
  PSTAT 197B DS CAPSTONE PROJECT     S22         NA
  PSTAT 197C DS CAPSTONE PROJECT     S22         47
   PSTAT 199 INDEPENDENT STUDIES     S22         19
 PSTAT 199RA INDEP RESEARCH ASST     S22         NA
    PSTAT 5A  UNDERSTANDING DATA     W22        278
    PSTAT 5H          STATISTICS     W22         NA
   PSTAT 5LS  STAT LIFE SCIENCES     W22        284
     PSTAT 8  TRANS DS PROB STAT     W22         NA
    PSTAT 10  DATA SCIENCE PRINC     W22        287
    PSTAT 99 INDEPENDENT STUDIES     W22         NA
   PSTAT 100        DS_CONC&ANLS     W22         88
   PSTAT 105  INTRO N-PARAM METH     W22         93
   PSTAT 109 STATISTICS FOR ECON     W22         NA
   PSTAT 115 BAYES DATA ANALYSIS     W22         81
  PSTAT 120A   PROB & STATISTICS     W22        229
  PSTAT 120B   PROB & STATISTICS     W22        241
  PSTAT 120C   PROB & STATISTICS     W22         NA
   PSTAT 122 DESIGN OF EXPERMNTS     W22        119
   PSTAT 123  SAMPLING TECHNIQUE     W22         NA
   PSTAT 126 REGRESSION ANALYSIS     W22        123
   PSTAT 127    ADV STATS MODELS     W22         91
   PSTAT 130    SAS BASE PROGRAM     W22         98
   PSTAT 131  STAT MACHINE LEARN     W22         76
   PSTAT 132 DATABASES FOR STATS     W22         NA
   PSTAT 134   STAT DATA SCIENCE     W22         66
   PSTAT 135  BIG DATA ANALYTICS     W22         NA
   PSTAT 140 STATISTICAL PROCESS     W22         NA
  PSTAT 160A  STOCHASTIC PROCESS     W22         77
  PSTAT 160B  STOCHASTIC PROCESS     W22         72
   PSTAT 170  INTRO MATH FINANCE     W22         69
   PSTAT 171   MATH COMPOUND INT     W22         68
  PSTAT 172A    ACTUARIAL STAT I     W22         60
  PSTAT 172B   ACTUARIAL STAT II     W22         NA
   PSTAT 173         RISK THEORY     W22         50
   PSTAT 174         TIME SERIES     W22         74
   PSTAT 175   SURVIVAL ANALYSIS     W22         NA
   PSTAT 176    ADV MATH FINANCE     W22         NA
   PSTAT 177      FINANCIAL RISK     W22         NA
  PSTAT 182T  ACTUARIAL TUTORIAL     W22          5
   PSTAT 183  ACTUARIAL CONCEPTS     W22         NA
   PSTAT 190        ULA TRAINING     W22         NA
   PSTAT 191       ULA PRACTICUM     W22         NA
   PSTAT 193 INTERNSHIP IN STATS     W22          4
   PSTAT 194  GRP STDY ADV STDNT     W22         NA
   PSTAT 195      SPECIAL TOPICS     W22         NA
   PSTAT 196   RESEARCH IN ACTSC     W22         NA
  PSTAT 197A    DS CAPSTONE PREP     W22         NA
  PSTAT 197B DS CAPSTONE PROJECT     W22         46
  PSTAT 197C DS CAPSTONE PROJECT     W22         NA
   PSTAT 199 INDEPENDENT STUDIES     W22          5
 PSTAT 199RA INDEP RESEARCH ASST     W22         NA
  • Could we have instead used Spring 2025 Enrollment, Winter 2025 Enrollment, etc. as our variables?

  • Well, we could… again, more on that during tomorrow’s lecture. (Spoiler: it’s not really a good idea.)

Another Dataset

Undergraduate PSTAT Course Enrollments

Moral of the Story

It is not always the case that the variables in a dataset are the same as the column names.

  • This starts to get into the structure of a dataset, so we’ll save a further discussion on this point for tomorrow’s lecture.
    • For now, I simply encourage you to think critically when trying to identify the variables in a particular dataset.
  • The good news is that, in many cases, the work is done for us: many datasets will come equipped with a data dictionary, which is a specification of all the variables in the dataset and a brief description of what they represent.

Variable Classification

Variable Classification

First Level

  • Notice how in both of the datasets we explored today, there were a few different types of variables.

  • For example, some variables have values that are numbers (e.g. the age of a cat; the enrollment total of a course; etc.) whereas others have values that are words (e.g. the species of a cat; the title of a course; etc.)

  • Indeed, at the highest level, variables are classified as either numerical or categorical.

    • Numerical variables are those whose values are numbers; categorical variables are those whose values are categories.

Variable Classification

First Level

Caution

It is a mistake to conclude that a variable is numerical solely because its recorded values are numbers.

  • For example, months can be encoded as either January, February, etc. or as 1, 2, 3.
    • Just because we’re using 1 to mean January doesn’t mean that a month variable is numerical - its possible values are still only categories, and hence it is a categorical variable.
    • 1 + 2 is 3, but January plus February is not March.
  • The better check is whether sums/differences of values have interpretive meaning- if so, the variable is numerical. Otherwise, the variable is categorical.

Your Turn!

Your Turn!

Turn to your neighbors, and come up with a few examples of numerical variables and a few examples of categorical variables.

05:00

Variable Classification

Second Level

  • Not all numerical variables are alike.

  • For example, consider the following two: “number of accidents recorded along a highway”, and “height of an individual.”

  • Both variables are numerical (sums/differences have interpretive meaning).

  • However, most of us have an intuitive feeling that the set of all possible values associated with “number of accidents recorded along a highway” is more restrictive than the set of possible values associated with “height of an individual.”

Variable Classification

Second Level

Definition

A numerical variable whose set of possible values is finite or countable is said to be discrete; a numerical variable whose set of possible values is uncountable is said to be continuous.

  • Note how this mirrors the definition of discrete and continuous random variables that you (hopefully) saw in PSTAT 120A!

  • Even within categorical variables, there’s a second level of classification. Consider: “letter grade” and “favorite color.”

  • A grade of A+ is better than a grade of A, which is better than a grade of A-, etc. whereas green is not inherently better than red, which is not inherently better than purple, etc.

Variable Classification

Second Level

Definition

A categorical variable whose set of possible values has an intrinsic order is said to be ordinal; a categorical variable whose set of possible values has no intrinsic order is said to be nominal.

data_classification cluster_main cluster_0 cluster_1 cluster_2 cluster_3 Data Variable numerical Numerical Data->numerical categorical Categorical Data->categorical continuous Continuous numerical->continuous discrete Discrete numerical->discrete nominal Nominal categorical->nominal ordinal Ordinal categorical->ordinal

Your Turn!

Your Turn!

For the variables you and your neighbor(s) came up with in the previous activity, classify them as discrete, continuous, ordinal, or nominal.

04:00

Next Time

  • We’ll continue our discussion on data.
    • Specifically, we’ll take a closer look at the structure (as opposed to semantics) of a dataset
    • We’ll then discuss a framework to unify the semantics and structure of a dataset.
  • Reminder: please start Homework 1 early!
    • Problem 1 is a Linear Algebra review, and Problem 2 combines Linear Algebra and PSTAT 120A (so you should be able to complete both problems already).
    • For problem 3, you’ll need to wait until Thursday’s lecture.
  • If you are able, please bring your laptops to tomorrow’s lecture.