- 1
- The data
- 2
- The mapping of variables to aesthetics
- 3
- The geoms (as many as necessary, possibly with additional/different aesthetics and mappings)
PSTAT 100: Lecture 04
Statistical Visalizations, Part II
Ethan P. Marzban
Department of Statistics and Applied Probability; UCSB
Summer Session A, 2025
The Grammar of Graphics
Most of us can probably make a graph pretty easily, with a pen, paper, and a ruler.
But what are the actual components that go into a visualization?
- This is an important question to answer in order to be able to make computers generate graphs and visualizations.
Hopefully everyone had a chance to at least skim through the paper that was linked as reading for today, so you should all know that one answer to this question can be found in the so-called grammar of graphics
First proposed by Leland Wilkinson in 1999, and then modified by Hadley Wickham in the 2000s.
The Grammar of Graphics
First, we need data (remember this from earlier this week?)
Next, we need to specify axes / a coordinate system
- What variable goes on the x-axis? What about the y-axis? Should we include a radial axis? Should we make a map?
Finally, we need geometric objects (shortened to geoms)
- Do we need bars or points? Lines or sectors? Etc.
Aesthetics are additional attributes of the geoms, to which variables can be mapped (e.g. coordinates of points, heights of bars, etc.)
- Be careful to distinguish the aesthetics from the aesthetic mappings - the latter is what maps the data to the former.
Common Aesthetics
The Grammar of Graphics
Example
- Note that (at least for this class), we are treating x- and y-coordinates as aesthetics.
The Grammar of Graphics
ggplot2
- The
ggplot2package inR(part of thetidyverse) uses precisely this framework to generate graphics.- In fact, the
ggstands for “grammar of graphics”
- In fact, the
The Grammar of Graphics
ggplot2
- 1
-
The dataframe is called
commute_times - 2
- We want Commute Distance on the horizontal axis
- 3
- We want Commute Time on the vertical axis
- 4
- We want points (i.e. we want to generate a scatterplot)
The Grammar of Graphics
ggplot2
Code
- 1
- Increase the point size
- 2
- Add a title
- 3
- Add a theme to the plot
World Bank Dataset
- The World Bank is a collection of organization aiming to study the effects of poverty worldwide.
- You can read more about them at their website.
- To motivate our discussions on visualizations, we’ll be taking a look at some data collected by the World Bank. The variables included are:
- Country Name
- Country Code (abbreviation)
- Continent
- Year of observation
- GDP (Gross Domestic Product)
- Female Life Expectancy at Birth
- Male Life Expectancy at Birth
- Total Life Expectancy at Birth
- Female Adult Literacy Rate
- Male Adult Literacy Rate
- Total Adult Literacy Rate
- Female Youth Literacy Rate
- Male Youth Literacy Rate
- Total Youth Literacy Rate
- Population
World Bank Dataset
Country Name Country Code Continent
1 Afghanistan AFG Asia
2 Afghanistan AFG Asia
3 Afghanistan AFG Asia
4 Afghanistan AFG Asia
5 Afghanistan AFG Asia
6 Afghanistan AFG Asia
7 Afghanistan AFG Asia
8 Afghanistan AFG Asia
9 Afghanistan AFG Asia
10 Afghanistan AFG Asia
11 Afghanistan AFG Asia
12 Albania ALB Europe
13 Albania ALB Europe
14 Albania ALB Europe
15 Albania ALB Europe
16 Albania ALB Europe
17 Albania ALB Europe
18 Albania ALB Europe
19 Albania ALB Europe
20 Albania ALB Europe
21 Albania ALB Europe
22 Albania ALB Europe
23 Algeria DZA Africa
24 Algeria DZA Africa
25 Algeria DZA Africa
26 Algeria DZA Africa
27 Algeria DZA Africa
28 Algeria DZA Africa
29 Algeria DZA Africa
30 Algeria DZA Africa
31 Algeria DZA Africa
32 Algeria DZA Africa
33 Algeria DZA Africa
34 American Samoa ASM North America
35 American Samoa ASM North America
36 American Samoa ASM North America
37 American Samoa ASM North America
38 American Samoa ASM North America
39 American Samoa ASM North America
40 American Samoa ASM North America
41 American Samoa ASM North America
42 American Samoa ASM North America
43 American Samoa ASM North America
44 American Samoa ASM North America
45 Andorra AND Europe
46 Andorra AND Europe
47 Andorra AND Europe
48 Andorra AND Europe
49 Andorra AND Europe
50 Andorra AND Europe
51 Andorra AND Europe
52 Andorra AND Europe
53 Andorra AND Europe
54 Andorra AND Europe
55 Andorra AND Europe
56 Angola AGO Africa
57 Angola AGO Africa
58 Angola AGO Africa
59 Angola AGO Africa
60 Angola AGO Africa
61 Angola AGO Africa
62 Angola AGO Africa
63 Angola AGO Africa
64 Angola AGO Africa
65 Angola AGO Africa
66 Angola AGO Africa
67 Antigua and Barbuda ATG North America
68 Antigua and Barbuda ATG North America
69 Antigua and Barbuda ATG North America
70 Antigua and Barbuda ATG North America
71 Antigua and Barbuda ATG North America
72 Antigua and Barbuda ATG North America
73 Antigua and Barbuda ATG North America
74 Antigua and Barbuda ATG North America
75 Antigua and Barbuda ATG North America
76 Antigua and Barbuda ATG North America
77 Antigua and Barbuda ATG North America
78 Argentina ARG South America
79 Argentina ARG South America
80 Argentina ARG South America
81 Argentina ARG South America
82 Argentina ARG South America
83 Argentina ARG South America
84 Argentina ARG South America
85 Argentina ARG South America
86 Argentina ARG South America
87 Argentina ARG South America
88 Argentina ARG South America
89 Armenia ARM Europe
90 Armenia ARM Europe
91 Armenia ARM Europe
92 Armenia ARM Europe
93 Armenia ARM Europe
94 Armenia ARM Europe
95 Armenia ARM Europe
96 Armenia ARM Europe
97 Armenia ARM Europe
98 Armenia ARM Europe
99 Armenia ARM Europe
100 Aruba ABW North America
Series Name 1960
1 GDP (current US$) NA
2 Life expectancy at birth, female (years) 3.354900e+01
3 Life expectancy at birth, male (years) 3.213600e+01
4 Life expectancy at birth, total (years) 3.279900e+01
5 Literacy rate, adult female (% of females ages 15 and above) NA
6 Literacy rate, adult male (% of males ages 15 and above) NA
7 Literacy rate, adult total (% of people ages 15 and above) NA
8 Literacy rate, youth female (% of females ages 15-24) NA
9 Literacy rate, youth male (% of males ages 15-24) NA
10 Literacy rate, youth total (% of people ages 15-24) NA
11 Population, total 9.035043e+06
12 GDP (current US$) NA
13 Life expectancy at birth, female (years) 5.887700e+01
14 Life expectancy at birth, male (years) 5.400500e+01
15 Life expectancy at birth, total (years) 5.641300e+01
16 Literacy rate, adult female (% of females ages 15 and above) NA
17 Literacy rate, adult male (% of males ages 15 and above) NA
18 Literacy rate, adult total (% of people ages 15 and above) NA
19 Literacy rate, youth female (% of females ages 15-24) NA
20 Literacy rate, youth male (% of males ages 15-24) NA
21 Literacy rate, youth total (% of people ages 15-24) NA
22 Population, total 1.608800e+06
23 GDP (current US$) 2.723615e+09
24 Life expectancy at birth, female (years) 4.385800e+01
25 Life expectancy at birth, male (years) 3.822500e+01
26 Life expectancy at birth, total (years) 4.083900e+01
27 Literacy rate, adult female (% of females ages 15 and above) NA
28 Literacy rate, adult male (% of males ages 15 and above) NA
29 Literacy rate, adult total (% of people ages 15 and above) NA
30 Literacy rate, youth female (% of females ages 15-24) NA
31 Literacy rate, youth male (% of males ages 15-24) NA
32 Literacy rate, youth total (% of people ages 15-24) NA
33 Population, total 1.142492e+07
34 GDP (current US$) NA
35 Life expectancy at birth, female (years) 6.710700e+01
36 Life expectancy at birth, male (years) 6.317600e+01
37 Life expectancy at birth, total (years) 6.505300e+01
38 Literacy rate, adult female (% of females ages 15 and above) NA
39 Literacy rate, adult male (% of males ages 15 and above) NA
40 Literacy rate, adult total (% of people ages 15 and above) NA
41 Literacy rate, youth female (% of females ages 15-24) NA
42 Literacy rate, youth male (% of males ages 15-24) NA
43 Literacy rate, youth total (% of people ages 15-24) NA
44 Population, total 2.013300e+04
45 GDP (current US$) NA
46 Life expectancy at birth, female (years) 7.508100e+01
47 Life expectancy at birth, male (years) 6.910900e+01
48 Life expectancy at birth, total (years) 7.209400e+01
49 Literacy rate, adult female (% of females ages 15 and above) NA
50 Literacy rate, adult male (% of males ages 15 and above) NA
51 Literacy rate, adult total (% of people ages 15 and above) NA
52 Literacy rate, youth female (% of females ages 15-24) NA
53 Literacy rate, youth male (% of males ages 15-24) NA
54 Literacy rate, youth total (% of people ages 15-24) NA
55 Population, total 9.510000e+03
56 GDP (current US$) NA
57 Life expectancy at birth, female (years) 3.973900e+01
58 Life expectancy at birth, male (years) 3.624800e+01
59 Life expectancy at birth, total (years) 3.793300e+01
60 Literacy rate, adult female (% of females ages 15 and above) NA
61 Literacy rate, adult male (% of males ages 15 and above) NA
62 Literacy rate, adult total (% of people ages 15 and above) NA
63 Literacy rate, youth female (% of females ages 15-24) NA
64 Literacy rate, youth male (% of males ages 15-24) NA
65 Literacy rate, youth total (% of people ages 15-24) NA
66 Population, total 5.231654e+06
67 GDP (current US$) NA
68 Life expectancy at birth, female (years) 6.475500e+01
69 Life expectancy at birth, male (years) 6.011700e+01
70 Life expectancy at birth, total (years) 6.263500e+01
71 Literacy rate, adult female (% of females ages 15 and above) NA
72 Literacy rate, adult male (% of males ages 15 and above) NA
73 Literacy rate, adult total (% of people ages 15 and above) NA
74 Literacy rate, youth female (% of females ages 15-24) NA
75 Literacy rate, youth male (% of males ages 15-24) NA
76 Literacy rate, youth total (% of people ages 15-24) NA
77 Population, total 5.560300e+04
78 GDP (current US$) NA
79 Life expectancy at birth, female (years) 6.778900e+01
80 Life expectancy at birth, male (years) 6.120200e+01
81 Life expectancy at birth, total (years) 6.424200e+01
82 Literacy rate, adult female (% of females ages 15 and above) NA
83 Literacy rate, adult male (% of males ages 15 and above) NA
84 Literacy rate, adult total (% of people ages 15 and above) NA
85 Literacy rate, youth female (% of females ages 15-24) NA
86 Literacy rate, youth male (% of males ages 15-24) NA
87 Literacy rate, youth total (% of people ages 15-24) NA
88 Population, total 2.038604e+07
89 GDP (current US$) NA
90 Life expectancy at birth, female (years) 6.215000e+01
91 Life expectancy at birth, male (years) 5.612300e+01
92 Life expectancy at birth, total (years) 5.906300e+01
93 Literacy rate, adult female (% of females ages 15 and above) NA
94 Literacy rate, adult male (% of males ages 15 and above) NA
95 Literacy rate, adult total (% of people ages 15 and above) NA
96 Literacy rate, youth female (% of females ages 15-24) NA
97 Literacy rate, youth male (% of males ages 15-24) NA
98 Literacy rate, youth total (% of people ages 15-24) NA
99 Population, total 1.863705e+06
100 GDP (current US$) NA
1961 1962 1963 1964 1965
1 NA NA NA NA NA
2 3.404300e+01 3.450200e+01 3.494500e+01 3.542800e+01 3.590000e+01
3 3.262600e+01 3.309800e+01 3.354300e+01 3.400400e+01 3.443800e+01
4 3.329100e+01 3.375700e+01 3.420100e+01 3.467300e+01 3.512400e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 9.214083e+06 9.404406e+06 9.604487e+06 9.814318e+06 1.003601e+07
12 NA NA NA NA NA
13 5.999500e+01 6.104700e+01 6.208600e+01 6.304800e+01 6.393400e+01
14 5.502800e+01 5.600000e+01 5.693800e+01 5.782400e+01 5.867700e+01
15 5.748800e+01 5.849400e+01 5.947900e+01 6.040400e+01 6.127300e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 1.659800e+06 1.711319e+06 1.762621e+06 1.814135e+06 1.864791e+06
23 2.434747e+09 2.001445e+09 2.702982e+09 2.909316e+09 3.136284e+09
24 4.377000e+01 4.270600e+01 4.360700e+01 4.342900e+01 4.327000e+01
25 3.819400e+01 3.681300e+01 4.267400e+01 4.254300e+01 4.242600e+01
26 4.079200e+01 3.952700e+01 4.314300e+01 4.298700e+01 4.284600e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 1.162888e+07 1.180077e+07 1.198212e+07 1.217981e+07 1.236598e+07
34 NA NA NA NA NA
35 6.791600e+01 6.842700e+01 6.856700e+01 6.845400e+01 6.821100e+01
36 6.362800e+01 6.388800e+01 6.406000e+01 6.410100e+01 6.404400e+01
37 6.564800e+01 6.600800e+01 6.616100e+01 6.613500e+01 6.599600e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 2.066600e+04 2.129800e+04 2.196600e+04 2.267300e+04 2.340600e+04
45 NA NA NA NA NA
46 7.574400e+01 7.637200e+01 7.687100e+01 7.735200e+01 7.768800e+01
47 6.945400e+01 6.973500e+01 6.992400e+01 7.017500e+01 7.038600e+01
48 7.257300e+01 7.299300e+01 7.329800e+01 7.362400e+01 7.385600e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 1.028300e+04 1.108600e+04 1.191500e+04 1.276400e+04 1.363400e+04
56 NA NA NA NA NA
57 3.988500e+01 4.021800e+01 4.050700e+01 4.081300e+01 4.112000e+01
58 3.426600e+01 3.448900e+01 3.472000e+01 3.499600e+01 3.523600e+01
59 3.690200e+01 3.716800e+01 3.741900e+01 3.770400e+01 3.796800e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 5.301583e+06 5.354310e+06 5.408320e+06 5.464187e+06 5.521981e+06
67 NA NA NA NA NA
68 6.552000e+01 6.623200e+01 6.700200e+01 6.778600e+01 6.858400e+01
69 6.076600e+01 6.139100e+01 6.203600e+01 6.272800e+01 6.340700e+01
70 6.333500e+01 6.399500e+01 6.469700e+01 6.542800e+01 6.617100e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 5.654000e+04 5.733600e+04 5.813800e+04 5.902000e+04 5.997000e+04
78 NA 2.445060e+10 1.827212e+10 2.560525e+10 2.834471e+10
79 6.823600e+01 6.828200e+01 6.857500e+01 6.853700e+01 6.881900e+01
80 6.152600e+01 6.147400e+01 6.165000e+01 6.160900e+01 6.178300e+01
81 6.463100e+01 6.461800e+01 6.485500e+01 6.481600e+01 6.505300e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 2.072628e+07 2.107254e+07 2.142170e+07 2.176945e+07 2.211263e+07
89 NA NA NA NA NA
90 6.259800e+01 6.303800e+01 6.346700e+01 6.388100e+01 6.427700e+01
91 5.653800e+01 5.694400e+01 5.733900e+01 5.771700e+01 5.807300e+01
92 5.949410e+01 5.991668e+01 6.032827e+01 6.072383e+01 6.109934e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 1.927484e+06 1.991689e+06 2.056023e+06 2.120135e+06 2.183635e+06
100 NA NA NA NA NA
1966 1967 1968 1969 1970
1 NA NA NA NA NA
2 3.638000e+01 3.685100e+01 3.728100e+01 3.775800e+01 3.826100e+01
3 3.487700e+01 3.532400e+01 3.582500e+01 3.628700e+01 3.674800e+01
4 3.558300e+01 3.604200e+01 3.651000e+01 3.697900e+01 3.746000e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.026640e+07 1.050596e+07 1.075692e+07 1.101741e+07 1.129013e+07
12 NA NA NA NA NA
13 6.481400e+01 6.564200e+01 6.647600e+01 6.723700e+01 6.794600e+01
14 5.954300e+01 6.036400e+01 6.115100e+01 6.188800e+01 6.258100e+01
15 6.214900e+01 6.297600e+01 6.378800e+01 6.453800e+01 6.523400e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 1.914573e+06 1.965598e+06 2.022272e+06 2.081695e+06 2.135479e+06
23 3.039859e+09 3.370870e+09 3.852147e+09 4.257253e+09 4.863527e+09
24 4.315500e+01 4.312200e+01 4.318900e+01 4.338100e+01 4.373800e+01
25 4.234700e+01 4.234300e+01 4.242600e+01 4.260600e+01 4.292600e+01
26 4.274500e+01 4.273100e+01 4.280600e+01 4.299100e+01 4.332800e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 1.259007e+07 1.287612e+07 1.317261e+07 1.347596e+07 1.378372e+07
34 NA NA NA NA NA
35 5.858300e+01 6.801900e+01 6.812800e+01 6.846500e+01 6.902000e+01
36 5.803300e+01 6.385200e+01 6.383000e+01 6.391800e+01 6.404600e+01
37 5.828400e+01 6.580700e+01 6.584700e+01 6.605000e+01 6.636400e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 2.413600e+04 2.486300e+04 2.561400e+04 2.637500e+04 2.702600e+04
45 NA NA NA NA 7.861771e+07
46 7.790900e+01 7.797900e+01 7.800200e+01 7.798800e+01 7.807500e+01
47 7.058300e+01 7.074100e+01 7.093400e+01 7.111100e+01 7.135300e+01
48 7.402000e+01 7.411900e+01 7.422000e+01 7.429600e+01 7.445200e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 1.462600e+04 1.583700e+04 1.717600e+04 1.855500e+04 1.997700e+04
56 NA NA NA NA NA
57 4.148700e+01 4.183700e+01 4.223000e+01 4.257700e+01 4.296400e+01
58 3.548000e+01 3.584900e+01 3.618000e+01 3.655900e+01 3.690800e+01
59 3.825800e+01 3.861600e+01 3.896800e+01 3.932900e+01 3.968800e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 5.581386e+06 5.641807e+06 5.702699e+06 5.763685e+06 5.852788e+06
67 NA NA NA NA NA
68 6.935300e+01 7.009300e+01 7.077800e+01 7.139700e+01 7.196600e+01
69 6.408500e+01 6.469800e+01 6.527800e+01 6.582900e+01 6.631500e+01
70 6.690200e+01 6.758600e+01 6.823000e+01 6.882700e+01 6.937100e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.090000e+04 6.183700e+04 6.280900e+04 6.381900e+04 6.452800e+04
78 2.863047e+10 2.425667e+10 2.643686e+10 3.125628e+10 3.158421e+10
79 6.909500e+01 6.928800e+01 6.919300e+01 6.913300e+01 6.956400e+01
80 6.215700e+01 6.212600e+01 6.177900e+01 6.155300e+01 6.216500e+01
81 6.539800e+01 6.546700e+01 6.523400e+01 6.508500e+01 6.564700e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 2.245389e+07 2.279906e+07 2.315058e+07 2.350871e+07 2.387833e+07
89 NA NA NA NA NA
90 6.465300e+01 6.500800e+01 6.534300e+01 6.565800e+01 6.595400e+01
91 5.840700e+01 5.871500e+01 5.899900e+01 5.925800e+01 5.949300e+01
92 6.145383e+01 6.178476e+01 6.209363e+01 6.237995e+01 6.264471e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 2.246159e+06 2.307492e+06 2.367319e+06 2.424030e+06 2.475633e+06
100 NA NA NA NA NA
1971 1972 1973 1974 1975
1 NA NA NA NA NA
2 3.875200e+01 3.925500e+01 3.977800e+01 4.029100e+01 4.081300e+01
3 3.720200e+01 3.768100e+01 3.821300e+01 3.873400e+01 3.926100e+01
4 3.793200e+01 3.842300e+01 3.895100e+01 3.946900e+01 3.999400e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.156767e+07 1.185370e+07 1.215800e+07 1.246913e+07 1.277395e+07
12 NA NA NA NA NA
13 6.861200e+01 6.924600e+01 6.984400e+01 7.040000e+01 7.091800e+01
14 6.324600e+01 6.387000e+01 6.444200e+01 6.495400e+01 6.542500e+01
15 6.589600e+01 6.652600e+01 6.710700e+01 6.763300e+01 6.812000e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 2.187853e+06 2.243126e+06 2.296752e+06 2.350124e+06 2.404831e+06
23 5.077183e+09 6.766744e+09 8.707859e+09 1.320987e+10 1.555790e+10
24 4.423400e+01 4.489400e+01 4.567900e+01 4.660700e+01 4.766900e+01
25 4.334400e+01 4.389500e+01 4.455300e+01 4.533700e+01 4.622100e+01
26 4.378200e+01 4.438400e+01 4.510200e+01 4.595300e+01 4.692100e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 1.409894e+07 1.442707e+07 1.477115e+07 1.513350e+07 1.567860e+07
34 NA NA NA NA NA
35 6.969600e+01 7.029400e+01 7.069800e+01 7.104000e+01 7.133100e+01
36 6.425800e+01 6.454100e+01 6.496000e+01 6.528900e+01 6.559400e+01
37 6.677000e+01 6.718600e+01 6.760400e+01 6.795000e+01 6.825600e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 2.753300e+04 2.799500e+04 2.843600e+04 2.887500e+04 2.939000e+04
45 8.940661e+07 1.134144e+08 1.508416e+08 1.865571e+08 2.201126e+08
46 7.819300e+01 7.846100e+01 7.875100e+01 7.907200e+01 7.939100e+01
47 7.158300e+01 7.185500e+01 7.208400e+01 7.231100e+01 7.251400e+01
48 7.461500e+01 7.486400e+01 7.509600e+01 7.534000e+01 7.556700e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 2.144200e+04 2.295700e+04 2.452300e+04 2.613000e+04 2.777300e+04
56 NA NA NA NA NA
57 4.331100e+01 4.370200e+01 4.404000e+01 4.441900e+01 4.417900e+01
58 3.731600e+01 3.770100e+01 3.814300e+01 3.853100e+01 3.793600e+01
59 4.007600e+01 4.046900e+01 4.087100e+01 4.126000e+01 4.081700e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 5.991102e+06 6.174262e+06 6.388528e+06 6.613367e+06 6.842947e+06
67 NA NA NA NA NA
68 7.248700e+01 7.295700e+01 7.337400e+01 7.377700e+01 7.414500e+01
69 6.678900e+01 6.722300e+01 6.763600e+01 6.802100e+01 6.837400e+01
70 6.986100e+01 7.030400e+01 7.071000e+01 7.109500e+01 7.144700e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.472900e+04 6.461500e+04 6.434200e+04 6.405800e+04 6.383900e+04
78 3.329320e+10 3.473300e+10 5.254400e+10 7.243678e+10 5.243865e+10
79 6.941700e+01 6.976400e+01 7.008700e+01 7.037100e+01 7.091300e+01
80 6.221000e+01 6.251700e+01 6.267100e+01 6.280800e+01 6.336700e+01
81 6.561900e+01 6.595300e+01 6.618600e+01 6.640500e+01 6.696500e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 2.425721e+07 2.464433e+07 2.504600e+07 2.546135e+07 2.587411e+07
89 NA NA NA NA NA
90 6.623200e+01 6.647500e+01 6.671500e+01 6.695900e+01 6.721700e+01
91 5.970500e+01 5.991400e+01 6.010800e+01 6.029700e+01 6.048300e+01
92 6.288890e+01 6.311449e+01 6.333093e+01 6.354676e+01 6.376788e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 2.525345e+06 2.577079e+06 2.630860e+06 2.686445e+06 2.743660e+06
100 NA NA NA NA NA
1976 1977 1978 1979 1980
1 NA NA NA NA NA
2 4.133300e+01 4.188000e+01 4.147900e+01 4.088100e+01 4.137900e+01
3 3.978700e+01 4.036300e+01 3.885500e+01 3.709000e+01 3.742800e+01
4 4.051800e+01 4.108200e+01 4.008600e+01 3.884400e+01 3.925800e+01
5 NA NA NA 5.000000e+00 NA
6 NA NA NA 3.000000e+01 NA
7 NA NA NA 1.800000e+01 NA
8 NA NA NA 1.100000e+01 NA
9 NA NA NA 4.600000e+01 NA
10 NA NA NA 3.000000e+01 NA
11 1.305985e+07 1.334076e+07 1.361144e+07 1.365557e+07 1.316931e+07
12 NA NA NA NA 1.578102e+09
13 7.139900e+01 7.185200e+01 7.226900e+01 7.259700e+01 7.296700e+01
14 6.586100e+01 6.627100e+01 6.662500e+01 6.682800e+01 6.704000e+01
15 6.857000e+01 6.899200e+01 6.936700e+01 6.961700e+01 6.990300e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 2.458526e+06 2.513546e+06 2.566266e+06 2.617832e+06 2.671997e+06
23 1.772824e+10 2.097211e+10 2.636449e+10 3.324371e+10 4.234583e+10
24 4.890300e+01 5.027900e+01 5.182200e+01 5.378000e+01 5.603100e+01
25 4.721900e+01 4.828600e+01 4.949300e+01 5.114200e+01 5.310400e+01
26 4.803400e+01 4.924900e+01 5.061500e+01 5.240900e+01 5.451200e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 1.640917e+07 1.701599e+07 1.750697e+07 1.803666e+07 1.860717e+07
34 NA NA NA NA NA
35 7.159000e+01 7.182200e+01 7.203100e+01 7.224000e+01 7.253800e+01
36 6.579500e+01 6.603000e+01 6.619800e+01 6.645100e+01 6.674700e+01
37 6.847500e+01 6.870100e+01 6.888100e+01 6.911400e+01 6.941300e+01
38 NA NA NA NA 9.700000e+01
39 NA NA NA NA 9.700000e+01
40 NA NA NA NA 9.700000e+01
41 NA NA NA NA 9.700000e+01
42 NA NA NA NA 9.800000e+01
43 NA NA NA NA 9.800000e+01
44 2.995900e+04 3.052100e+04 3.107600e+04 3.161100e+04 3.240300e+04
45 2.272839e+08 2.539979e+08 3.080203e+08 4.115487e+08 4.463778e+08
46 7.978500e+01 8.015400e+01 8.056900e+01 8.097500e+01 8.137000e+01
47 7.278700e+01 7.305400e+01 7.335700e+01 7.366300e+01 7.395600e+01
48 7.586900e+01 7.615400e+01 7.648800e+01 7.681900e+01 7.713700e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 2.943600e+04 3.109700e+04 3.273500e+04 3.430600e+04 3.578200e+04
56 NA NA NA NA 5.930503e+09
57 4.423300e+01 4.458500e+01 4.488900e+01 4.518400e+01 4.547000e+01
58 3.788200e+01 3.831200e+01 3.870000e+01 3.906200e+01 3.941100e+01
59 4.081200e+01 4.121500e+01 4.157300e+01 4.191300e+01 4.224200e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 7.074664e+06 7.317829e+06 7.576734e+06 7.847207e+06 8.133872e+06
67 NA 7.749630e+07 8.803333e+07 1.095852e+08 1.324407e+08
68 7.450200e+01 7.488300e+01 7.526200e+01 7.559500e+01 7.585300e+01
69 6.872700e+01 6.906800e+01 6.940300e+01 6.972900e+01 7.002200e+01
70 7.179400e+01 7.214900e+01 7.250000e+01 7.282300e+01 7.309400e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.376200e+04 6.386200e+04 6.403800e+04 6.427400e+04 6.451300e+04
78 5.116950e+10 5.678100e+10 8.904945e+10 6.925233e+10 7.696192e+10
79 7.098300e+01 7.155900e+01 7.170800e+01 7.200100e+01 7.204700e+01
80 6.340600e+01 6.394400e+01 6.453500e+01 6.507200e+01 6.528200e+01
81 6.703000e+01 6.759500e+01 6.799900e+01 6.843400e+01 6.857600e+01
82 NA NA NA NA 9.400000e+01
83 NA NA NA NA 9.400000e+01
84 NA NA NA NA 9.400000e+01
85 NA NA NA NA 9.700000e+01
86 NA NA NA NA 9.600000e+01
87 NA NA NA NA 9.700000e+01
88 2.628228e+07 2.670180e+07 2.713216e+07 2.756890e+07 2.801160e+07
89 NA NA NA NA NA
90 6.748800e+01 6.778400e+01 6.808800e+01 6.839800e+01 6.870600e+01
91 6.068100e+01 6.089200e+01 6.113400e+01 6.141400e+01 6.174100e+01
92 6.400149e+01 6.425395e+01 6.452620e+01 6.482083e+01 6.513856e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 2.818165e+06 2.912827e+06 3.012807e+06 3.078501e+06 3.107415e+06
100 NA NA NA NA NA
1981 1982 1983 1984 1985
1 NA NA NA NA NA
2 4.169500e+01 3.951800e+01 4.009300e+01 3.642200e+01 3.710100e+01
3 3.743300e+01 3.325100e+01 3.359900e+01 2.782300e+01 2.839300e+01
4 3.940600e+01 3.605800e+01 3.651700e+01 3.147300e+01 3.213200e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.193758e+07 1.099138e+07 1.091798e+07 1.119022e+07 1.142685e+07
12 1.808177e+09 1.861163e+09 1.881413e+09 1.857338e+09 1.897050e+09
13 7.328700e+01 7.361800e+01 7.397000e+01 7.432900e+01 7.468400e+01
14 6.721000e+01 6.744100e+01 6.765800e+01 6.786700e+01 6.811500e+01
15 7.014500e+01 7.042500e+01 7.070500e+01 7.098400e+01 7.128200e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 2.726056e+06 2.784278e+06 2.843960e+06 2.904429e+06 2.964762e+06
23 4.434859e+10 4.520717e+10 4.880137e+10 5.369855e+10 5.793787e+10
24 5.908400e+01 6.124700e+01 6.274200e+01 6.408600e+01 6.543100e+01
25 5.587600e+01 5.804800e+01 5.984800e+01 6.142700e+01 6.293800e+01
26 5.742200e+01 5.959400e+01 6.125100e+01 6.272200e+01 6.415500e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 1.922070e+07 1.987235e+07 2.055812e+07 2.127197e+07 2.200854e+07
34 NA NA NA NA NA
35 7.287500e+01 7.307000e+01 7.318700e+01 7.327500e+01 7.351100e+01
36 6.705400e+01 6.734300e+01 6.759300e+01 6.781900e+01 6.800700e+01
37 6.973100e+01 6.997500e+01 7.016300e+01 7.032600e+01 7.053200e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 3.358400e+04 3.490900e+04 3.627100e+04 3.766700e+04 3.910300e+04
45 3.889833e+08 3.759147e+08 3.278500e+08 3.300731e+08 3.467427e+08
46 8.169000e+01 8.197100e+01 8.219600e+01 8.240400e+01 8.257100e+01
47 7.419900e+01 7.440300e+01 7.454800e+01 7.465400e+01 7.471900e+01
48 7.739100e+01 7.761700e+01 7.778700e+01 7.791600e+01 7.800600e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 3.716900e+04 3.876400e+04 4.056500e+04 4.227300e+04 4.382500e+04
56 5.550483e+09 5.550483e+09 5.784342e+09 6.131475e+09 7.554065e+09
57 4.575000e+01 4.601600e+01 4.545600e+01 4.568600e+01 4.589100e+01
58 3.973800e+01 4.005400e+01 3.892300e+01 3.921300e+01 3.948000e+01
59 4.255600e+01 4.285700e+01 4.197200e+01 4.224500e+01 4.249500e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 8.435607e+06 8.751648e+06 9.082983e+06 9.425917e+06 9.779120e+06
67 1.493778e+08 1.664259e+08 1.848481e+08 2.121926e+08 2.463444e+08
68 7.605000e+01 7.623700e+01 7.638100e+01 7.649900e+01 7.657300e+01
69 7.028800e+01 7.051900e+01 7.070300e+01 7.084000e+01 7.092600e+01
70 7.332000e+01 7.352500e+01 7.368400e+01 7.380800e+01 7.387300e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.466500e+04 6.478500e+04 6.493400e+04 6.488200e+04 6.459100e+04
78 7.867684e+10 8.430749e+10 1.039791e+11 1.169151e+11 8.815089e+10
79 7.243600e+01 7.255700e+01 7.270600e+01 7.277800e+01 7.340200e+01
80 6.545500e+01 6.555900e+01 6.600200e+01 6.605400e+01 6.647400e+01
81 6.885800e+01 6.897300e+01 6.929000e+01 6.935300e+01 6.987900e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 2.846396e+07 2.892426e+07 2.939133e+07 2.986309e+07 3.033644e+07
89 NA NA NA NA NA
90 6.901100e+01 6.931900e+01 6.962100e+01 6.991500e+01 7.020100e+01
91 6.212200e+01 6.254800e+01 6.299900e+01 6.342600e+01 6.378600e+01
92 6.548249e+01 6.585093e+01 6.622924e+01 6.659137e+01 6.691527e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 3.135349e+06 3.163144e+06 3.191539e+06 3.224547e+06 3.260432e+06
100 NA NA NA NA NA
1986 1987 1988 1989 1990
1 NA NA NA NA NA
2 4.207200e+01 4.260300e+01 4.596200e+01 4.704200e+01 4.770300e+01
3 3.527000e+01 3.560100e+01 4.074200e+01 4.213200e+01 4.271200e+01
4 3.840000e+01 3.883100e+01 4.323800e+01 4.449600e+01 4.511800e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.142007e+07 1.138782e+07 1.152330e+07 1.187409e+07 1.204566e+07
12 2.097326e+09 2.080796e+09 2.051236e+09 2.253090e+09 2.028554e+09
13 7.513800e+01 7.547700e+01 7.572600e+01 7.595600e+01 7.619500e+01
14 6.843700e+01 6.872700e+01 6.894000e+01 6.917400e+01 6.941200e+01
15 7.166500e+01 7.198100e+01 7.221700e+01 7.245700e+01 7.271000e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 3.022635e+06 3.083605e+06 3.142336e+06 3.227943e+06 3.286542e+06
23 6.369201e+10 6.674582e+10 5.908940e+10 5.563472e+10 6.204851e+10
24 6.648600e+01 6.718900e+01 6.765700e+01 6.807900e+01 6.824200e+01
25 6.411600e+01 6.511300e+01 6.617900e+01 6.685600e+01 6.708800e+01
26 6.527300e+01 6.613000e+01 6.691000e+01 6.746100e+01 6.765800e+01
27 NA 3.600000e+01 NA NA NA
28 NA 6.300000e+01 NA NA NA
29 NA 5.000000e+01 NA NA NA
30 NA 6.200000e+01 NA NA NA
31 NA 8.600000e+01 NA NA NA
32 NA 7.400000e+01 NA NA NA
33 2.274550e+07 2.344362e+07 2.410954e+07 2.475448e+07 2.537581e+07
34 NA NA NA NA NA
35 7.388700e+01 7.429100e+01 7.466300e+01 7.485200e+01 7.524200e+01
36 6.801700e+01 6.793400e+01 6.777100e+01 6.773900e+01 6.777200e+01
37 7.070400e+01 7.082800e+01 7.088300e+01 7.092900e+01 7.110700e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 4.057100e+04 4.207200e+04 4.361500e+04 4.519100e+04 4.664000e+04
45 4.819960e+08 6.112999e+08 7.214259e+08 7.954896e+08 1.028990e+09
46 8.277500e+01 8.296000e+01 8.311700e+01 8.323500e+01 8.338700e+01
47 7.479000e+01 7.484500e+01 7.503300e+01 7.528100e+01 7.581500e+01
48 7.810700e+01 7.818900e+01 7.836400e+01 7.855700e+01 7.896100e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 4.573400e+04 4.765300e+04 4.941600e+04 5.062000e+04 5.259700e+04
56 7.072536e+09 8.084412e+09 8.769837e+09 1.020178e+10 1.122952e+10
57 4.607200e+01 4.462400e+01 4.512500e+01 4.531500e+01 4.543000e+01
58 3.975900e+01 3.744100e+01 3.823400e+01 3.846800e+01 3.863900e+01
59 4.273900e+01 4.078600e+01 4.147100e+01 4.169800e+01 4.185400e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 1.013945e+07 1.049786e+07 1.086129e+07 1.123856e+07 1.162636e+07
67 2.975370e+08 3.468407e+08 4.113741e+08 4.551481e+08 4.786926e+08
68 7.660300e+01 7.659000e+01 7.653200e+01 7.632800e+01 7.633800e+01
69 7.096900e+01 7.097700e+01 7.094400e+01 7.081800e+01 7.079600e+01
70 7.389300e+01 7.387300e+01 7.381100e+01 7.362800e+01 7.360200e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.427600e+04 6.394600e+04 6.362300e+04 6.332500e+04 6.306600e+04
78 1.058724e+11 1.088109e+11 1.268902e+11 7.662973e+10 1.413526e+11
79 7.381000e+01 7.421900e+01 7.462300e+01 7.503900e+01 7.487800e+01
80 6.685200e+01 6.725600e+01 6.763200e+01 6.800800e+01 6.834700e+01
81 7.028100e+01 7.069900e+01 7.109700e+01 7.150200e+01 7.161500e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 3.081198e+07 3.129176e+07 3.178053e+07 3.227095e+07 3.275590e+07
89 NA NA NA NA 2.256863e+09
90 7.047500e+01 7.073700e+01 5.356100e+01 7.123300e+01 7.146100e+01
91 6.403800e+01 6.414200e+01 5.168500e+01 6.398100e+01 6.382400e+01
92 6.717800e+01 6.735907e+01 5.260012e+01 6.751856e+01 6.754937e+01
93 NA NA NA 9.800000e+01 NA
94 NA NA NA 9.900000e+01 NA
95 NA NA NA 9.900000e+01 NA
96 NA NA NA 1.000000e+02 NA
97 NA NA NA 1.000000e+02 NA
98 NA NA NA 1.000000e+02 NA
99 3.294847e+06 3.328520e+06 3.355125e+06 3.443100e+06 3.552128e+06
100 4.055866e+08 4.877095e+08 5.966480e+08 6.955307e+08 7.648045e+08
1991 1992 1993 1994 1995
1 NA NA NA NA NA
2 4.828200e+01 4.960700e+01 5.229600e+01 5.313500e+01 5.369400e+01
3 4.295900e+01 4.376500e+01 4.975500e+01 4.888300e+01 5.053600e+01
4 4.552100e+01 4.656900e+01 5.102100e+01 5.096900e+01 5.210300e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.223888e+07 1.327897e+07 1.494317e+07 1.625079e+07 1.706584e+07
12 1.099559e+09 6.521750e+08 1.185315e+09 1.880951e+09 2.392765e+09
13 7.645200e+01 7.672000e+01 7.700000e+01 7.720600e+01 7.740700e+01
14 6.970500e+01 7.001400e+01 7.038000e+01 7.056600e+01 7.073400e+01
15 7.300100e+01 7.330300e+01 7.363800e+01 7.383700e+01 7.402200e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 3.266790e+06 3.247039e+06 3.227287e+06 3.207536e+06 3.187784e+06
23 4.571568e+10 4.800313e+10 4.994558e+10 4.254318e+10 4.176429e+10
24 6.851200e+01 6.872700e+01 6.913900e+01 6.921900e+01 6.953500e+01
25 6.690100e+01 6.677000e+01 6.654800e+01 6.552400e+01 6.600300e+01
26 6.769200e+01 6.772500e+01 6.779700e+01 6.728400e+01 6.769100e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 2.598793e+07 2.662857e+07 2.727705e+07 2.788728e+07 2.847019e+07
34 NA NA NA NA NA
35 7.555100e+01 7.578400e+01 7.566200e+01 7.555400e+01 7.542200e+01
36 6.788300e+01 6.803400e+01 6.816100e+01 6.828500e+01 6.837500e+01
37 7.131200e+01 7.151100e+01 7.154000e+01 7.156900e+01 7.156500e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 4.788200e+04 4.903800e+04 5.015900e+04 5.125100e+04 5.231600e+04
45 1.106891e+09 1.209992e+09 1.007090e+09 1.017544e+09 1.178745e+09
46 8.347100e+01 8.360900e+01 8.382300e+01 8.408500e+01 8.429400e+01
47 7.636700e+01 7.702100e+01 7.754900e+01 7.807100e+01 7.820700e+01
48 7.934600e+01 7.979400e+01 8.018600e+01 8.058700e+01 8.080400e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 5.666700e+04 6.020000e+04 6.327200e+04 6.461200e+04 6.391200e+04
56 1.060378e+10 8.307811e+09 5.768720e+09 4.438321e+09 5.538749e+09
57 4.684400e+01 4.556300e+01 4.672300e+01 4.774500e+01 4.816000e+01
58 4.099100e+01 3.924300e+01 3.822700e+01 3.981900e+01 4.414500e+01
59 4.381200e+01 4.226700e+01 4.219000e+01 4.356700e+01 4.613900e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 1.202353e+07 1.242371e+07 1.282714e+07 1.324976e+07 1.369978e+07
67 5.043074e+08 5.251037e+08 5.656333e+08 6.250519e+08 6.160148e+08
68 7.622000e+01 7.612800e+01 7.616800e+01 7.634700e+01 7.652600e+01
69 7.069500e+01 7.062200e+01 7.059400e+01 7.062100e+01 7.060700e+01
70 7.347200e+01 7.338600e+01 7.339000e+01 7.349300e+01 7.357600e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.338700e+04 6.440400e+04 6.558700e+04 6.684300e+04 6.818900e+04
78 1.897200e+11 2.287789e+11 2.367417e+11 2.574400e+11 2.580318e+11
79 7.534400e+01 7.549600e+01 7.570700e+01 7.590900e+01 7.617000e+01
80 6.868100e+01 6.869100e+01 6.889200e+01 6.950100e+01 6.952100e+01
81 7.202000e+01 7.209600e+01 7.230300e+01 7.273200e+01 7.286400e+01
82 9.600000e+01 NA NA NA NA
83 9.600000e+01 NA NA NA NA
84 9.600000e+01 NA NA NA NA
85 9.900000e+01 NA NA NA NA
86 9.800000e+01 NA NA NA NA
87 9.800000e+01 NA NA NA NA
88 3.323029e+07 3.369353e+07 3.415272e+07 3.461349e+07 3.507002e+07
89 2.069870e+09 1.272835e+09 1.201313e+09 1.315159e+09 1.468317e+09
90 7.169900e+01 7.189600e+01 7.214400e+01 7.237500e+01 7.261900e+01
91 6.374900e+01 6.374000e+01 6.400100e+01 6.436400e+01 6.482800e+01
92 6.762705e+01 6.771854e+01 6.797320e+01 6.827180e+01 6.862849e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 3.613977e+06 3.571861e+06 3.453332e+06 3.364610e+06 3.307581e+06
100 8.720670e+08 9.586592e+08 1.083240e+09 1.245810e+09 1.320670e+09
1996 1997 1998 1999 2000
1 NA NA NA NA 3.521418e+09
2 5.442600e+01 5.472000e+01 5.439200e+01 5.596600e+01 5.655500e+01
3 5.126000e+01 5.172500e+01 5.063600e+01 5.310200e+01 5.346300e+01
4 5.283000e+01 5.321200e+01 5.248700e+01 5.453200e+01 5.500500e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 1.776327e+07 1.845209e+07 1.916000e+07 1.988778e+07 2.013033e+07
12 3.199641e+09 2.258514e+09 2.545965e+09 3.212122e+09 3.480355e+09
13 7.753300e+01 7.705200e+01 7.772500e+01 7.782200e+01 7.792600e+01
14 7.079800e+01 6.986600e+01 7.109200e+01 7.140500e+01 7.180400e+01
15 7.411300e+01 7.338300e+01 7.435700e+01 7.456800e+01 7.482600e+01
16 NA NA NA NA NA
17 NA NA NA NA NA
18 NA NA NA NA NA
19 NA NA NA NA NA
20 NA NA NA NA NA
21 NA NA NA NA NA
22 3.168033e+06 3.148281e+06 3.128530e+06 3.108778e+06 3.089027e+06
23 4.694155e+10 4.817761e+10 4.818778e+10 4.864067e+10 5.479040e+10
24 6.991800e+01 7.051700e+01 7.103100e+01 7.151000e+01 7.194400e+01
25 6.665000e+01 6.732400e+01 6.775000e+01 6.875400e+01 6.928900e+01
26 6.821900e+01 6.885900e+01 6.932700e+01 7.008800e+01 7.057600e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 2.903304e+07 2.957930e+07 3.005413e+07 3.047435e+07 3.090389e+07
34 NA NA NA NA NA
35 7.532200e+01 7.524600e+01 7.489000e+01 7.459100e+01 7.435100e+01
36 6.846800e+01 6.857100e+01 6.871300e+01 6.882200e+01 6.891100e+01
37 7.157600e+01 7.160600e+01 7.154200e+01 7.148400e+01 7.144300e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 5.335300e+04 5.436200e+04 5.533400e+04 5.624800e+04 5.685500e+04
45 1.224024e+09 1.180646e+09 1.211954e+09 1.240295e+09 1.432606e+09
46 8.451000e+01 8.471300e+01 8.486400e+01 8.506800e+01 8.509800e+01
47 7.839200e+01 7.847900e+01 7.857700e+01 7.885600e+01 7.935300e+01
48 8.100900e+01 8.114500e+01 8.128000e+01 8.155000e+01 8.186300e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 6.398400e+04 6.470000e+04 6.538200e+04 6.571000e+04 6.568500e+04
56 7.526447e+09 7.648377e+09 6.506230e+09 6.152923e+09 9.129595e+09
57 4.840200e+01 4.868400e+01 4.804700e+01 4.900300e+01 4.913200e+01
58 4.445700e+01 4.471600e+01 4.295400e+01 4.279900e+01 4.396300e+01
59 4.641800e+01 4.668800e+01 4.545200e+01 4.580800e+01 4.650100e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 1.417097e+07 1.466041e+07 1.515937e+07 1.566724e+07 1.619487e+07
67 6.791111e+08 7.343926e+08 7.897630e+08 8.355148e+08 9.005519e+08
68 7.694900e+01 7.730400e+01 7.751700e+01 7.786400e+01 7.829500e+01
69 7.071800e+01 7.078200e+01 7.082600e+01 7.099100e+01 7.125900e+01
70 7.383900e+01 7.404500e+01 7.418700e+01 7.445600e+01 7.481900e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 6.961200e+04 7.105300e+04 7.241200e+04 7.366600e+04 7.491200e+04
78 2.721498e+11 2.928590e+11 2.989482e+11 2.835230e+11 2.842038e+11
79 7.643300e+01 7.683800e+01 7.687600e+01 7.707500e+01 7.728800e+01
80 6.965600e+01 6.995000e+01 6.993500e+01 7.026300e+01 7.049800e+01
81 7.305600e+01 7.340700e+01 7.341200e+01 7.368300e+01 7.391000e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 3.551379e+07 3.594779e+07 3.637286e+07 3.679468e+07 3.721398e+07
89 1.596969e+09 1.639492e+09 1.893726e+09 1.845482e+09 1.911564e+09
90 7.286500e+01 7.311800e+01 7.339700e+01 7.368700e+01 7.580000e+01
91 6.533100e+01 6.584700e+01 6.637300e+01 6.687700e+01 7.010000e+01
92 6.900612e+01 6.939383e+01 6.979934e+01 7.019895e+01 7.288049e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA 1.000000e+02
97 NA NA NA NA 1.000000e+02
98 NA NA NA NA 1.000000e+02
99 3.278735e+06 3.246289e+06 3.208401e+06 3.167286e+06 3.221100e+06
100 1.379888e+09 1.531844e+09 1.665363e+09 1.722905e+09 1.873453e+09
2001 2002 2003 2004 2005
1 2.813572e+09 3.825701e+09 4.520947e+09 5.224897e+09 6.203257e+09
2 5.708900e+01 5.744200e+01 5.847200e+01 5.907300e+01 5.958800e+01
3 5.394100e+01 5.498600e+01 5.584900e+01 5.651900e+01 5.688000e+01
4 5.551100e+01 5.622500e+01 5.717100e+01 5.781000e+01 5.824700e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 2.028431e+07 2.137812e+07 2.273305e+07 2.356065e+07 2.440457e+07
12 3.922101e+09 4.348068e+09 5.611496e+09 7.184686e+09 8.052077e+09
13 7.803100e+01 7.814200e+01 7.832900e+01 7.875300e+01 7.930300e+01
14 7.220400e+01 7.252900e+01 7.286400e+01 7.324200e+01 7.366300e+01
15 7.508300e+01 7.529900e+01 7.555700e+01 7.595100e+01 7.642700e+01
16 9.800000e+01 NA NA NA NA
17 9.900000e+01 NA NA NA NA
18 9.900000e+01 NA NA NA NA
19 9.900000e+01 NA NA NA 9.949000e+01
20 9.900000e+01 NA NA NA NA
21 9.900000e+01 NA NA NA NA
22 3.060173e+06 3.051010e+06 3.039616e+06 3.026939e+06 3.011487e+06
23 5.941340e+10 6.151610e+10 7.348226e+10 9.191368e+10 1.070466e+11
24 7.229500e+01 7.284200e+01 7.302700e+01 7.364200e+01 7.396200e+01
25 6.982300e+01 7.050500e+01 7.083700e+01 7.147800e+01 7.176000e+01
26 7.102500e+01 7.164400e+01 7.190600e+01 7.253600e+01 7.283600e+01
27 NA 6.000000e+01 NA NA NA
28 NA 7.900000e+01 NA NA NA
29 NA 7.000000e+01 NA NA NA
30 NA 8.600000e+01 NA NA NA
31 NA 9.400000e+01 NA NA NA
32 NA 9.000000e+01 NA NA NA
33 3.133122e+07 3.175084e+07 3.217582e+07 3.262829e+07 3.310925e+07
34 NA 5.120000e+08 5.240000e+08 5.090000e+08 5.000000e+08
35 7.448300e+01 7.465700e+01 7.459000e+01 7.512500e+01 7.512500e+01
36 6.904100e+01 6.923100e+01 6.918300e+01 6.979100e+01 6.997300e+01
37 7.157300e+01 7.175500e+01 7.169800e+01 7.227700e+01 7.238200e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 5.705300e+04 5.706200e+04 5.697100e+04 5.681800e+04 5.661700e+04
45 1.548266e+09 1.764280e+09 2.366942e+09 2.900245e+09 3.161084e+09
46 8.516700e+01 8.513000e+01 8.511600e+01 8.497900e+01 8.527200e+01
47 7.977800e+01 8.026600e+01 8.073400e+01 8.099000e+01 8.124000e+01
48 8.216200e+01 8.244800e+01 8.271800e+01 8.281500e+01 8.308600e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 6.585200e+04 6.650600e+04 6.948600e+04 7.432500e+04 7.742100e+04
56 8.936079e+09 1.528559e+10 1.781270e+10 2.355206e+10 3.697090e+10
57 5.004700e+01 5.036700e+01 5.218100e+01 5.307400e+01 5.405100e+01
58 4.416200e+01 4.544600e+01 4.825800e+01 4.917000e+01 5.020300e+01
59 4.703200e+01 4.787400e+01 5.021800e+01 5.112300e+01 5.213000e+01
60 5.400000e+01 NA NA NA NA
61 8.300000e+01 NA NA NA NA
62 6.700000e+01 NA NA NA NA
63 6.300000e+01 NA NA NA NA
64 8.400000e+01 NA NA NA NA
65 7.200000e+01 NA NA NA NA
66 1.674721e+07 1.732770e+07 1.794371e+07 1.860042e+07 1.929116e+07
67 8.775148e+08 8.979889e+08 9.479556e+08 1.026181e+09 1.143715e+09
68 7.859200e+01 7.851900e+01 7.827600e+01 7.817900e+01 7.829800e+01
69 7.153100e+01 7.181800e+01 7.215300e+01 7.227200e+01 7.223600e+01
70 7.510800e+01 7.523700e+01 7.531300e+01 7.532900e+01 7.536400e+01
71 9.900000e+01 NA NA NA NA
72 9.800000e+01 NA NA NA NA
73 9.900000e+01 NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 7.606900e+04 7.703200e+04 7.788400e+04 7.871900e+04 7.961100e+04
78 2.686968e+11 9.772400e+10 1.275870e+11 1.646579e+11 1.987371e+11
79 7.764200e+01 7.791100e+01 7.780800e+01 7.817700e+01 7.863200e+01
80 7.063700e+01 7.070400e+01 7.079600e+01 7.150000e+01 7.176700e+01
81 7.415400e+01 7.431200e+01 7.430700e+01 7.487100e+01 7.523100e+01
82 9.700000e+01 NA NA NA NA
83 9.700000e+01 NA NA NA NA
84 9.700000e+01 NA NA NA NA
85 9.900000e+01 NA NA NA NA
86 9.900000e+01 NA NA NA NA
87 9.900000e+01 NA NA NA NA
88 3.762482e+07 3.802935e+07 3.842428e+07 3.881592e+07 3.921679e+07
89 2.118468e+09 2.376335e+09 2.807061e+09 3.576615e+09 4.900470e+09
90 7.610000e+01 7.590000e+01 7.590000e+01 7.610000e+01 7.620000e+01
91 7.000000e+01 6.990000e+01 6.990000e+01 7.010000e+01 7.010000e+01
92 7.297561e+01 7.282683e+01 7.282683e+01 7.302683e+01 7.307561e+01
93 9.900000e+01 NA NA NA NA
94 1.000000e+02 NA NA NA NA
95 9.900000e+01 NA NA NA NA
96 1.000000e+02 NA NA NA NA
97 1.000000e+02 NA NA NA NA
98 1.000000e+02 NA NA NA NA
99 3.211800e+06 3.199800e+06 3.182500e+06 3.164900e+06 3.146400e+06
100 1.896457e+09 1.961844e+09 2.044112e+09 2.254831e+09 2.360017e+09
2006 2007 2008 2009 2010
1 6.971758e+09 9.747886e+09 1.010930e+10 1.241615e+10 1.585667e+10
2 6.012300e+01 6.080400e+01 6.142800e+01 6.179100e+01 6.228300e+01
3 5.697400e+01 5.712200e+01 5.798400e+01 5.868100e+01 5.909700e+01
4 5.855300e+01 5.895600e+01 5.970800e+01 6.024800e+01 6.070200e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 2.542409e+07 2.590985e+07 2.648262e+07 2.746610e+07 2.828409e+07
12 8.896075e+09 1.067732e+10 1.288135e+10 1.204421e+10 1.192693e+10
13 7.994300e+01 8.058400e+01 8.107600e+01 8.128200e+01 8.110800e+01
14 7.418300e+01 7.492200e+01 7.553100e+01 7.584200e+01 7.582500e+01
15 7.699400e+01 7.769100e+01 7.824800e+01 7.850900e+01 7.841400e+01
16 NA NA 9.500000e+01 NA NA
17 NA NA 9.700000e+01 NA NA
18 NA NA 9.600000e+01 NA NA
19 NA NA 9.900000e+01 9.661000e+01 NA
20 NA NA 9.900000e+01 9.482000e+01 NA
21 NA NA 9.900000e+01 9.568000e+01 NA
22 2.992547e+06 2.970017e+06 2.947314e+06 2.927519e+06 2.913021e+06
23 1.230843e+11 1.424827e+11 1.803838e+11 1.503173e+11 1.777851e+11
24 7.428300e+01 7.455600e+01 7.482700e+01 7.507400e+01 7.531900e+01
25 7.200300e+01 7.219200e+01 7.246400e+01 7.272100e+01 7.301700e+01
26 7.311600e+01 7.334600e+01 7.361800e+01 7.387100e+01 7.414400e+01
27 6.400000e+01 NA 6.800000e+01 NA NA
28 8.100000e+01 NA 8.300000e+01 NA NA
29 7.300000e+01 NA 7.500000e+01 NA NA
30 8.900000e+01 NA 9.200000e+01 NA NA
31 9.400000e+01 NA 9.600000e+01 NA NA
32 9.200000e+01 NA 9.400000e+01 NA NA
33 3.362351e+07 3.418942e+07 3.481696e+07 3.549044e+07 3.618824e+07
34 4.930000e+08 5.180000e+08 5.600000e+08 6.750000e+08 5.730000e+08
35 7.504300e+01 7.494700e+01 7.503000e+01 7.312300e+01 7.519900e+01
36 7.006100e+01 7.007200e+01 7.011600e+01 6.878900e+01 7.024000e+01
37 7.239700e+01 7.236500e+01 7.243000e+01 7.083900e+01 7.258700e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 5.637400e+04 5.611300e+04 5.582800e+04 5.552800e+04 5.522800e+04
45 3.459338e+09 3.957625e+09 4.102319e+09 3.688976e+09 3.449926e+09
46 8.559300e+01 8.597600e+01 8.629200e+01 8.661100e+01 8.668400e+01
47 8.150100e+01 8.167600e+01 8.184600e+01 8.203700e+01 8.213800e+01
48 8.337400e+01 8.363200e+01 8.385500e+01 8.410000e+01 8.419700e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 7.958500e+04 8.187700e+04 8.349500e+04 8.388800e+04 8.070600e+04
56 5.238103e+10 6.526642e+10 8.853867e+10 7.030720e+10 8.379947e+10
57 5.481100e+01 5.604100e+01 5.716200e+01 5.812900e+01 5.922100e+01
58 5.110700e+01 5.234500e+01 5.338600e+01 5.430800e+01 5.525300e+01
59 5.296500e+01 5.420000e+01 5.528100e+01 5.622500e+01 5.724200e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 2.001528e+07 2.077856e+07 2.157866e+07 2.241477e+07 2.329482e+07
67 1.303548e+09 1.487300e+09 1.557541e+09 1.386444e+09 1.298256e+09
68 7.857500e+01 7.881700e+01 7.916500e+01 7.950900e+01 7.987900e+01
69 7.225400e+01 7.243200e+01 7.277800e+01 7.304900e+01 7.330500e+01
70 7.550600e+01 7.572000e+01 7.607500e+01 7.638600e+01 7.670100e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 8.060400e+04 8.170400e+04 8.291200e+04 8.417300e+04 8.532000e+04
78 2.325573e+11 2.875305e+11 3.615580e+11 3.329765e+11 4.236274e+11
79 7.843700e+01 7.792500e+01 7.857700e+01 7.859300e+01 7.873200e+01
80 7.202100e+01 7.157400e+01 7.219200e+01 7.244900e+01 7.254200e+01
81 7.527900e+01 7.478300e+01 7.542800e+01 7.557700e+01 7.568000e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 3.962212e+07 4.001676e+07 4.042415e+07 4.085483e+07 4.128869e+07
89 6.384452e+09 9.206301e+09 1.166204e+10 8.647937e+09 9.260286e+09
90 7.600000e+01 7.610000e+01 7.630000e+01 7.630000e+01 7.640000e+01
91 6.980000e+01 6.980000e+01 7.000000e+01 7.000000e+01 7.010000e+01
92 7.282439e+01 7.287317e+01 7.307317e+01 7.307317e+01 7.317317e+01
93 NA NA NA NA NA
94 NA NA NA NA NA
95 NA NA NA NA NA
96 NA NA NA NA NA
97 NA NA NA NA NA
98 NA NA NA NA NA
99 3.127100e+06 3.107400e+06 3.087100e+06 3.066000e+06 3.044800e+06
100 2.469783e+09 2.677641e+09 2.843025e+09 2.553793e+09 2.453597e+09
2011 2012 2013 2014 2015
1 1.780510e+10 1.990733e+10 2.014642e+10 2.049713e+10 1.913422e+10
2 6.285200e+01 6.334400e+01 6.381400e+01 6.400900e+01 6.417800e+01
3 5.962500e+01 6.009900e+01 6.053400e+01 6.049500e+01 6.036300e+01
4 6.125000e+01 6.173500e+01 6.218800e+01 6.226000e+01 6.227000e+01
5 1.700000e+01 NA NA NA 1.708624e+01
6 4.500000e+01 NA NA NA 5.021210e+01
7 3.100000e+01 NA NA NA 3.375384e+01
8 3.200000e+01 NA NA NA 2.548416e+01
9 6.200000e+01 NA NA NA 5.773505e+01
10 4.700000e+01 NA NA NA 3.582084e+01
11 2.934771e+07 3.056003e+07 3.162270e+07 3.279252e+07 3.383176e+07
12 1.289076e+10 1.231983e+10 1.277622e+10 1.322815e+10 1.138685e+10
13 8.091600e+01 8.058900e+01 8.038700e+01 8.026700e+01 8.045100e+01
14 7.579200e+01 7.566000e+01 7.566600e+01 7.583000e+01 7.628100e+01
15 7.830300e+01 7.808400e+01 7.799500e+01 7.802900e+01 7.835800e+01
16 9.600000e+01 9.600000e+01 NA NA NA
17 9.800000e+01 9.800000e+01 NA NA NA
18 9.700000e+01 9.700000e+01 NA NA NA
19 9.900000e+01 9.900000e+01 NA NA NA
20 9.900000e+01 9.900000e+01 NA NA NA
21 9.900000e+01 9.900000e+01 NA NA NA
22 2.905195e+06 2.900401e+06 2.895092e+06 2.889104e+06 2.880703e+06
23 2.183319e+11 2.271437e+11 2.297014e+11 2.389427e+11 1.874939e+11
24 7.554700e+01 7.576900e+01 7.598600e+01 7.618300e+01 7.637700e+01
25 7.326600e+01 7.349300e+01 7.368000e+01 7.385000e+01 7.399200e+01
26 7.438300e+01 7.460900e+01 7.480900e+01 7.499200e+01 7.515900e+01
27 NA NA NA NA NA
28 NA NA NA NA NA
29 NA NA NA NA NA
30 NA NA NA NA NA
31 NA NA NA NA NA
32 NA NA NA NA NA
33 3.690338e+07 3.764617e+07 3.841417e+07 3.920503e+07 4.001953e+07
34 5.700000e+08 6.400000e+08 6.380000e+08 6.430000e+08 6.730000e+08
35 7.528600e+01 7.537200e+01 7.541800e+01 7.529600e+01 7.526800e+01
36 7.029600e+01 7.030900e+01 7.037900e+01 7.033000e+01 7.029400e+01
37 7.266200e+01 7.270900e+01 7.276900e+01 7.268700e+01 7.265400e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 5.489500e+04 5.448900e+04 5.400600e+04 5.346600e+04 5.287800e+04
45 3.629134e+09 3.188653e+09 3.193513e+09 3.271686e+09 2.789881e+09
46 8.669200e+01 8.666900e+01 8.665200e+01 8.662600e+01 8.658400e+01
47 8.218800e+01 8.227100e+01 8.236100e+01 8.249300e+01 8.258100e+01
48 8.429600e+01 8.433400e+01 8.440600e+01 8.448500e+01 8.453200e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 7.778300e+04 7.683400e+04 7.519400e+04 7.373700e+04 7.217400e+04
56 1.117897e+11 1.280529e+11 1.323391e+11 1.359668e+11 9.049642e+10
57 6.021000e+01 6.115700e+01 6.200900e+01 6.272800e+01 6.341200e+01
58 5.597600e+01 5.667700e+01 5.740400e+01 5.806800e+01 5.868000e+01
59 5.809300e+01 5.891600e+01 5.970500e+01 6.039600e+01 6.104200e+01
60 NA NA NA 5.300000e+01 5.192598e+01
61 NA NA NA 8.000000e+01 8.377277e+01
62 NA NA NA 6.600000e+01 6.623586e+01
63 NA NA NA 7.100000e+01 6.742760e+01
64 NA NA NA 8.500000e+01 8.396919e+01
65 NA NA NA 7.700000e+01 7.566081e+01
66 2.421835e+07 2.517739e+07 2.616562e+07 2.716077e+07 2.815780e+07
67 1.281337e+09 1.327107e+09 1.325426e+09 1.378830e+09 1.437756e+09
68 8.023400e+01 8.037900e+01 8.032500e+01 8.013800e+01 7.997300e+01
69 7.357900e+01 7.358800e+01 7.353700e+01 7.343800e+01 7.353600e+01
70 7.702300e+01 7.710000e+01 7.705000e+01 7.691200e+01 7.689200e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 8.633200e+04 8.726000e+04 8.806400e+04 8.876500e+04 8.940900e+04
78 5.301581e+11 5.459824e+11 5.520251e+11 5.263197e+11 5.947493e+11
79 7.940200e+01 7.867200e+01 7.862300e+01 7.915000e+01 7.979500e+01
80 7.273900e+01 7.285100e+01 7.296300e+01 7.330300e+01 7.336700e+01
81 7.610000e+01 7.580200e+01 7.582900e+01 7.626800e+01 7.660000e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 4.173066e+07 4.216172e+07 4.258246e+07 4.302407e+07 4.347701e+07
89 1.014211e+10 1.061932e+10 1.112146e+10 1.160951e+10 1.055334e+10
90 7.730000e+01 7.750000e+01 7.790000e+01 7.810000e+01 7.820000e+01
91 7.050000e+01 7.090000e+01 7.150000e+01 7.180000e+01 7.170000e+01
92 7.381707e+01 7.411951e+01 7.462195e+01 7.487317e+01 7.487073e+01
93 1.000000e+02 NA NA NA NA
94 1.000000e+02 NA NA NA NA
95 1.000000e+02 NA NA NA NA
96 1.000000e+02 NA NA NA NA
97 1.000000e+02 NA NA NA NA
98 1.000000e+02 NA NA NA NA
99 3.027900e+06 3.024100e+06 3.022000e+06 3.013800e+06 3.004600e+06
100 2.637859e+09 2.615208e+09 2.727850e+09 2.790850e+09 2.962907e+09
2016 2017 2018 2019 2020
1 1.811657e+10 1.875346e+10 1.805322e+10 1.879944e+10 1.995593e+10
2 6.464000e+01 6.560600e+01 6.594200e+01 6.614400e+01 6.465600e+01
3 6.066100e+01 5.938800e+01 5.917500e+01 5.991000e+01 5.845500e+01
4 6.264600e+01 6.240600e+01 6.244300e+01 6.294100e+01 6.145400e+01
5 NA NA NA NA NA
6 NA NA NA NA NA
7 NA NA NA NA NA
8 NA NA NA NA NA
9 NA NA NA NA NA
10 NA NA NA NA NA
11 3.470061e+07 3.568894e+07 3.674304e+07 3.785612e+07 3.906898e+07
12 1.186120e+10 1.301973e+10 1.537951e+10 1.558511e+10 1.524146e+10
13 8.062500e+01 8.079500e+01 8.100100e+01 8.106000e+01 8.034500e+01
14 7.666200e+01 7.699700e+01 7.744800e+01 7.783400e+01 7.542900e+01
15 7.864300e+01 7.890000e+01 7.923800e+01 7.946700e+01 7.782400e+01
16 NA 9.904904e+01 NA NA NA
17 NA 9.857200e+01 NA NA NA
18 NA 9.881623e+01 NA NA NA
19 NA 9.952556e+01 NA NA NA
20 NA 9.858999e+01 NA NA NA
21 NA 9.902406e+01 NA NA NA
22 2.876101e+06 2.873457e+06 2.866376e+06 2.854191e+06 2.837849e+06
23 1.807638e+11 1.898809e+11 1.945545e+11 1.934597e+11 1.648734e+11
24 7.657000e+01 7.675000e+01 7.692800e+01 7.709100e+01 7.494300e+01
25 7.410600e+01 7.417700e+01 7.425500e+01 7.435000e+01 7.173300e+01
26 7.531000e+01 7.543100e+01 7.555500e+01 7.568200e+01 7.325700e+01
27 NA NA 7.532297e+01 7.421020e+01 NA
28 NA NA 8.742296e+01 NA NA
29 NA NA 8.140784e+01 NA NA
30 NA NA 9.725216e+01 9.798970e+01 NA
31 NA NA 9.759406e+01 6.479000e+01 NA
32 NA NA 9.742652e+01 7.403000e+01 NA
33 4.085072e+07 4.168930e+07 4.250504e+07 4.329455e+07 4.404209e+07
34 6.710000e+08 6.120000e+08 6.390000e+08 6.470000e+08 7.210000e+08
35 7.530500e+01 7.558800e+01 7.568700e+01 7.572300e+01 7.568200e+01
36 7.024000e+01 7.030400e+01 7.021100e+01 7.010500e+01 6.999500e+01
37 7.264000e+01 7.280100e+01 7.279400e+01 7.275100e+01 7.267200e+01
38 NA NA NA NA NA
39 NA NA NA NA NA
40 NA NA NA NA NA
41 NA NA NA NA NA
42 NA NA NA NA NA
43 NA NA NA NA NA
44 5.224500e+04 5.158600e+04 5.090800e+04 5.020900e+04 4.976100e+04
45 2.896610e+09 3.000162e+09 3.218420e+09 3.155149e+09 2.891001e+09
46 8.646800e+01 8.632200e+01 8.619600e+01 8.610100e+01 8.384000e+01
47 8.256900e+01 8.246200e+01 8.235900e+01 8.218300e+01 7.582300e+01
48 8.448900e+01 8.435900e+01 8.424200e+01 8.409800e+01 7.941800e+01
49 NA NA NA NA NA
50 NA NA NA NA NA
51 NA NA NA NA NA
52 NA NA NA NA NA
53 NA NA NA NA NA
54 NA NA NA NA NA
55 7.218100e+04 7.376300e+04 7.516200e+04 7.647400e+04 7.738000e+04
56 5.276162e+10 7.369015e+10 7.945069e+10 7.089796e+10 4.850156e+10
57 6.400900e+01 6.452700e+01 6.505700e+01 6.550600e+01 6.577400e+01
58 5.923700e+01 5.972700e+01 6.019900e+01 6.060900e+01 6.050900e+01
59 6.161900e+01 6.212200e+01 6.262200e+01 6.305100e+01 6.311600e+01
60 NA NA NA NA NA
61 NA NA NA NA NA
62 NA NA NA NA NA
63 NA NA NA NA NA
64 NA NA NA NA NA
65 NA NA NA NA NA
66 2.918307e+07 3.023484e+07 3.129716e+07 3.237563e+07 3.345113e+07
67 1.489693e+09 1.531152e+09 1.661530e+09 1.725352e+09 1.410796e+09
68 7.992300e+01 7.988000e+01 7.988700e+01 7.984400e+01 7.981300e+01
69 7.371100e+01 7.385900e+01 7.404000e+01 7.414300e+01 7.415700e+01
70 7.696800e+01 7.703000e+01 7.713200e+01 7.716800e+01 7.716100e+01
71 NA NA NA NA NA
72 NA NA NA NA NA
73 NA NA NA NA NA
74 NA NA NA NA NA
75 NA NA NA NA NA
76 NA NA NA NA NA
77 8.996900e+04 9.046800e+04 9.092600e+04 9.136400e+04 9.184600e+04
78 5.575323e+11 6.436284e+11 5.248199e+11 4.477547e+11 3.857405e+11
79 7.913100e+01 7.920400e+01 7.950500e+01 7.943900e+01 7.878300e+01
80 7.304400e+01 7.379100e+01 7.395100e+01 7.416300e+01 7.298100e+01
81 7.610500e+01 7.654300e+01 7.677000e+01 7.684700e+01 7.587800e+01
82 NA NA NA NA NA
83 NA NA NA NA NA
84 NA NA NA NA NA
85 NA NA NA NA NA
86 NA NA NA NA NA
87 NA NA NA NA NA
88 4.390031e+07 4.428889e+07 4.465488e+07 4.497346e+07 4.519196e+07
89 1.054614e+10 1.152746e+10 1.245794e+10 1.361929e+10 1.264170e+10
90 7.830000e+01 7.870000e+01 7.900000e+01 7.950000e+01 7.860000e+01
91 7.160000e+01 7.190000e+01 7.240000e+01 7.310000e+01 6.840000e+01
92 7.486829e+01 7.521707e+01 7.561951e+01 7.622195e+01 7.337561e+01
93 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
94 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
95 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
96 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
97 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
98 1.000000e+02 1.000000e+02 NA NA 1.000000e+02
99 2.992300e+06 2.979400e+06 2.969000e+06 2.962500e+06 2.961500e+06
100 2.983635e+09 3.092429e+09 3.276184e+09 3.395799e+09 2.481857e+09
2021 2022 2023 2024
1 1.426000e+10 1.449724e+10 1.723305e+10 NA
2 6.407900e+01 6.723600e+01 6.753600e+01 NA
3 5.705200e+01 6.394100e+01 6.446700e+01 NA
4 6.041700e+01 6.561700e+01 6.603500e+01 NA
5 2.300000e+01 2.659656e+01 NA NA
6 5.200000e+01 NA NA NA
7 3.700000e+01 NA NA NA
8 4.200000e+01 4.417171e+01 NA NA
9 7.100000e+01 8.340000e+01 NA NA
10 5.600000e+01 6.266000e+01 NA NA
11 4.000041e+07 4.057884e+07 4.145476e+07 NA
12 1.803201e+10 1.901724e+10 2.354718e+10 NA
13 7.900200e+01 8.078100e+01 8.144600e+01 NA
14 7.474200e+01 7.675100e+01 7.772800e+01 NA
15 7.684400e+01 7.876900e+01 7.960200e+01 NA
16 NA 9.830000e+01 NA NA
17 NA 9.870000e+01 NA NA
18 NA 9.850000e+01 NA NA
19 NA 9.990000e+01 NA NA
20 NA 9.910000e+01 NA NA
21 NA 9.950000e+01 NA NA
22 2.811666e+06 2.777689e+06 2.745972e+06 NA
23 1.862312e+11 2.256385e+11 2.476262e+11 NA
24 7.665000e+01 7.759200e+01 7.769600e+01 NA
25 7.384500e+01 7.474000e+01 7.489500e+01 NA
26 7.520800e+01 7.612900e+01 7.626100e+01 NA
27 NA NA NA NA
28 NA NA NA NA
29 NA NA NA NA
30 NA NA NA NA
31 NA NA NA NA
32 NA NA NA NA
33 4.476110e+07 4.547739e+07 4.616422e+07 NA
34 7.500000e+08 8.710000e+08 NA NA
35 7.573000e+01 7.579400e+01 7.583800e+01 NA
36 7.002300e+01 7.005500e+01 7.020200e+01 NA
37 7.270800e+01 7.275200e+01 7.285200e+01 NA
38 NA NA NA NA
39 NA NA NA NA
40 NA NA NA NA
41 NA NA NA NA
42 NA NA NA NA
43 NA NA NA NA
44 4.922500e+04 4.834200e+04 4.752100e+04 NA
45 3.324648e+09 3.380613e+09 3.785067e+09 NA
46 8.467800e+01 8.607500e+01 8.610700e+01 NA
47 8.021600e+01 8.208300e+01 8.210000e+01 NA
48 8.233100e+01 8.401600e+01 8.404100e+01 NA
49 NA NA NA NA
50 NA NA NA NA
51 NA NA NA NA
52 NA NA NA NA
53 NA NA NA NA
54 NA NA NA NA
55 7.836400e+04 7.970500e+04 8.085600e+04 NA
56 6.650513e+10 1.043997e+11 8.482465e+10 NA
57 6.544100e+01 6.675300e+01 6.714400e+01 NA
58 6.049800e+01 6.174800e+01 6.209900e+01 NA
59 6.295800e+01 6.424600e+01 6.461700e+01 NA
60 NA 6.250000e+01 NA NA
61 NA 8.280000e+01 NA NA
62 NA 7.240000e+01 NA NA
63 NA 8.070000e+01 NA NA
64 NA 8.590000e+01 NA NA
65 NA 8.330000e+01 NA NA
66 3.453243e+07 3.563503e+07 3.674991e+07 NA
67 1.601367e+09 1.867733e+09 2.033085e+09 NA
68 7.975700e+01 8.015400e+01 8.029400e+01 NA
69 7.429500e+01 7.446100e+01 7.454900e+01 NA
70 7.719700e+01 7.748300e+01 7.759800e+01 NA
71 NA NA NA NA
72 NA NA NA NA
73 NA NA NA NA
74 NA NA NA NA
75 NA NA NA NA
76 NA NA NA NA
77 9.234900e+04 9.284000e+04 9.331600e+04 NA
78 4.865641e+11 6.327901e+11 6.460753e+11 NA
79 7.686000e+01 7.831800e+01 7.987500e+01 NA
80 7.111300e+01 7.324900e+01 7.480500e+01 NA
81 7.394800e+01 7.580600e+01 7.739500e+01 NA
82 NA NA NA NA
83 NA NA NA NA
84 NA NA NA NA
85 NA NA NA NA
86 NA NA NA NA
87 NA NA NA NA
88 4.531228e+07 4.540790e+07 4.553840e+07 NA
89 1.387891e+10 1.951351e+10 2.408575e+10 NA
90 7.740000e+01 7.830000e+01 8.100000e+01 NA
91 6.740000e+01 7.140000e+01 7.410000e+01 NA
92 7.227805e+01 7.476585e+01 7.746585e+01 NA
93 NA NA NA NA
94 NA NA NA NA
95 NA NA NA NA
96 NA NA NA NA
97 NA NA NA NA
98 NA NA NA NA
99 2.962300e+06 2.969200e+06 2.990900e+06 NA
100 2.929447e+09 3.279344e+09 3.648573e+09 NAWorld Bank Dataset
A Couple of Review Questions
- Is the dataframe tidy?
- If not, what operation(s) are needed to tidy the dataframe?
Answers:
- The dataframe is not tidy.
- We need to both
melt(to get the years in their own column) andpivot(to split the series names into separate columns; you’ll get practice with this in lab today)
World Bank Dataset
Tidying
Code
# A tibble: 100 × 15
`Country Name` `Country Code` Continent Year `GDP (current US$)`
<chr> <chr> <chr> <fct> <dbl>
1 Afghanistan AFG Asia 1960 NA
2 Albania ALB Europe 1960 NA
3 Algeria DZA Africa 1960 2723615451.
4 American Samoa ASM North America 1960 NA
5 Andorra AND Europe 1960 NA
6 Angola AGO Africa 1960 NA
7 Antigua and Barbuda ATG North America 1960 NA
8 Argentina ARG South America 1960 NA
9 Armenia ARM Europe 1960 NA
10 Aruba ABW North America 1960 NA
# ℹ 90 more rows
# ℹ 10 more variables: `Life expectancy at birth, female (years)` <dbl>,
# `Life expectancy at birth, male (years)` <dbl>,
# `Life expectancy at birth, total (years)` <dbl>,
# `Literacy rate, adult female (% of females ages 15 and above)` <dbl>,
# `Literacy rate, adult male (% of males ages 15 and above)` <dbl>,
# `Literacy rate, adult total (% of people ages 15 and above)` <dbl>, …World Bank Dataset
GDP vs. Life Expectancy, in 2014
World Bank Dataset
GDP vs. Life Expectancy, in 2014
It’s difficult to read this plot; the points are all clustered together.
- This is because
GDPhas a huge spread!
- This is because
As such, it will be beneficial to apply a transformation to the vertical axis.
Specifically, let’s see what happens if we compare log(GDP) to Total Life Expectancy.
World Bank Dataset
GDP vs. Life Expectancy, in 2014
World Bank Dataset
Variations across continents?
From this last plot, it appears as though, on average, higher GDPs correspond to higher life expectancies at birth.
Question: how (if at all) does this relationship change across continents?
- In other words, how can we incorporate information from the
Continentvariable into our plot?
- In other words, how can we incorporate information from the
Answer: using aesthetics!
- For example, we could color code each point based on the continent it belongs to.
World Bank Dataset
Variations across continents?
Code
wb_tidy %>%
filter(
Year == "2014"
) %>%
ggplot(aes(x = `Life expectancy at birth, total (years)`,
y = `GDP (current US$)`)) +
geom_point(aes(colour = Continent), size = 3) +
theme_minimal(base_size = 18) +
ggtitle("GDP vs. Life Expectancy", subtitle = "In 2014") +
scale_y_log10() + ylab("log(GDP), in USD") +
labs(colour = "Continent")
World Bank Dataset
Variations across continents?
Code
wb_tidy %>%
filter(
Year == "2014"
) %>%
ggplot(aes(x = `Life expectancy at birth, total (years)`,
y = `GDP (current US$)`)) +
geom_point(aes(colour = Continent,
shape = Continent), size = 3) +
theme_minimal(base_size = 18) +
ggtitle("GDP vs. Life Expectancy", subtitle = "In 2014") +
scale_y_log10() + ylab("log(GDP), in USD") +
labs(colour = "Continent")
World Bank Dataset
Variations across continents?
Okay, that’s a start!
- We now have information about continents displayed in our graph.
- Note how neat that is - we have three variables displayed on a single graph!
But, this plot is difficult to read; the continents are all layered on top of each other.
A useful trick to overcome this is called facetting, where we essentially break our plot up into a collection of plots.
In
ggplot2, facetting is relatively easy, using eitherfacet_wrap()orfacet_grid().
World Bank Dataset
Variations across continents?
Code
wb_tidy %>%
filter(
Year == "2014"
) %>%
ggplot(aes(x = `Life expectancy at birth, total (years)`,
y = `GDP (current US$)`)) +
geom_point(size = 3) +
facet_wrap(~Continent) +
theme_minimal(base_size = 18) +
ggtitle("GDP vs. Life Expectancy", subtitle = "In 2014") +
scale_y_log10() + ylab("log(GDP), in USD") +
labs(colour = "Continent")
Some Takeaways
- Hopefully this mini case study illustrated a few things:
- The beauty (again) of tidy data
- How we can encode multivariate information into a plot using aesthetics
- How transformations can mitigate the effects of skew
- How faceting can be used to overcome “busy” plots
- As another example, we can explore the
mtcarsdataset (which is one of the datasets that comes pre-installed withR)- Collected in 1974 by the Motor Trend US magazine, this dataset contains information on 32 different automobiles (including things like miles per gallon, number of cylinders, gross horsepower, etc.)
mtcars
Check Your Understanding
- How many variables are being compared?
- What aesthetic is each mapped to?
Theory of Visualization
Principles of Good Visualization
Setting Goals
When setting out to make a plot, it’s important to be intentional about our goals.
There are two main types of plots: exploratory, and presentation-quality.
- Summarize trends/patterns before performing more sophisticated statistical analyses
- Details not too important; quantity over quality
- Highly curated for maximal impact and understandability
- Curate for communication; quality over quantity
Principles of Good Visualizations
Tips and Tricks
Here are some tips I’ve found useful when crafting visualizations
- Keep things simple. You can (and in many cases should) try to communicate as much information as is effective. But, don’t take it to an extreme.
- 3D-Styling is almost NEVER effective. As neat and “cool” as 3D barplots might be, the 3D-styling elements often obfuscate the plot’s true meaning
- Beware of Scales and Areas. We;ll talk about this one more in a bit - spoiler alert, pie charts are a notoriously bad graphic!
Principles of Good Visualizations
Tips and Tricks
- Label Axes, and Title your Plots. This one should (hopefully) be self-explanatory, but make sure you are using descriptive (but not overly complex) labels for your axes, and make sure your plots are titled.
- Interpret your plots. All too often I see “floating” plots - that is, figures that appear mysteriously and suddenly with no explanation whatsoever. No matter how self-explanatory you think your plot is, make sure you actively describe it and its conclusions somewhere in your report.
More on Color
Color Scales
Qualitative
There are three main types of color scales: qualitative, sequential, and diverging.
Colors in a qualitative scale are meant to look visually different from one another, with no order, while still being “equal”.
- Good when trying to color according to a categorial (i.e. qualitative) variable
Color Scales
Qualitative Color Scale
Source: Fundamentals of Data Visualization, by Claus Wilke
Color Scales
Sequential
A sequential color scale ranges from light to dark (or dark to light).
Colors in a sequential scale are designed to convey an ordering, or hierarchy of values.
- Use when there is a natural direction, but not necessarily a meaningful “middle point”
- Can be based on a single hue, or across multiple hues
- More akin to what we colloquially call “gradients”
Color Scales
Sequential Color Scale
Source: Fundamentals of Data Visualization, by Claus Wilke
Color Scales
Diverging Color Scale
- Colors in a diverging scale are designed to convey an ordering, or hierarchy of values in two directions (positive or negative)
- Accomplished by effectively “stitching” together two sequential scales at a common, neutral midpoint.
- By construction, the midpoint is naturally highlighted so only use a diverging scale if there is a natural middle point (or if you want to highlight the two extremes).
Color Scales
Diverging Color Scale
Source: Fundamentals of Data Visualization, by Claus Wilke
Color Scales
Source: Fundamentals of Data Visualization, by Claus Wilke
Color Scales
Source: Fundamentals of Data Visualization, by Claus Wilke
Your Turn!
Your Turn!
Suppose we want to use color to encode information about the following variables. Identify the scale/s that is/are most appropriate.
Distinguishing between different Majors
Distinguishing between different unemployment rates (i.e. on a map)
Distinguishing between different countries’ GDPs, and highlighting a change that occurs as GDP increases.
03:00
CVD and Accessibility
Especially when it comes to presentation-oriented graphics, accessibility is key.
One thing to keep in mind that many readers may suffer from Color-Vision Deficiency (CVD; aka colorblindness), and may not be able to easily perceive differences in colors.
- Deuteranomaly: difficulty perceiving green
- Protanomaly: difficulty perceiving red
- Tritanomaly: difficulty perceiving blue
Trichromatic persons (i.e. people with no colorblindness) possess all three retinal cone cell types (and have cone cell types that function “as expected”, and are therefore able to process and perceive red, green, and blue light
Image Source: https://www.aao.org/eye-health/anatomy/cones
CVD and Accessibility
CVD and Accessibility
CVD and Accessibility
The Okabe-Ito Palette
- Another resource: https://www.color-blindness.com/coblis-color-blindness-simulator/
Interlude
Color Specification Schemes
A quick interlude- some of you may be wondering what all these codes and hashtags mean.
There are a few different color specification schemes (i.e. ways to express colors in a more rigorous manner).
RGB: “Red Green Blue”. Represents each color as a triple of values (between 0 and 255), specifying the amount of Red, Green, and Blue to be included in the hue
- E.g.
(255, 0, 0): pure red - E.g.
(127, 0, 127): what color would this make?
- E.g.
Interlude
Color Specification Schemes
- Nice! But, not always predictable.
- RGB specifications can be as few as 3 digits long, or as many as 9 digits long.
- The hexadecimal (more colloquially referred to as hex) color specification scheme also specifies the amount of red, green, and blue in a hue, but does so in six characters.
- Each digit is written using hexadecimal notation
- 0 – 9 correspond to our “familiar” values 0 through 9
- A – F correspond to “familiar” (decimal) values 10 through 15.
Interlude
Hex Color Scheme
Interlude
Hex Color Scheme
Next Time
And Coming Up
On Monday, we’ll start exploring other (numerical) ways of summarizing data.
In lab today, we’ll cover a brief introduction to databases, and ways to combine two or more dataframes together.
Please don’t forget to finish Homework 1, which is due 11:59pm this Sunday!!!
- You have all the information needed to complete all the problems now.
- For the final problem, keep in mind the principles of visualization we talked about today!
PSTAT 100 - Data Science: Concepts and Analysis, Summer 2025 with Ethan P. Marzban