Data in which the values represent some numerical quantity are referred to as quantitative data. For example, here is a dataset that contains savings rates along with other demographic variables for 50 countries during 1960-70.
sr pop15 pop75 dpi ddpi
Australia 11.43 29.35 2.87 2329.68 2.87
Austria 12.07 23.32 4.41 1507.99 3.93
Belgium 13.17 23.80 4.43 2108.47 3.82
Bolivia 5.75 41.89 1.67 189.13 0.22
Brazil 12.88 42.19 0.83 728.47 4.56
Canada 8.79 31.72 2.85 2982.88 2.43
Chile 0.60 39.74 1.34 662.86 2.67
China 11.90 44.75 0.67 289.52 6.51
Colombia 4.98 46.64 1.06 276.65 3.08
Costa Rica 10.78 47.64 1.14 471.24 2.80
Denmark 16.85 24.42 3.93 2496.53 3.99
Ecuador 3.59 46.31 1.19 287.77 2.19
Finland 11.24 27.84 2.37 1681.25 4.32
France 12.64 25.06 4.70 2213.82 4.52
Germany 12.55 23.31 3.35 2457.12 3.44
Greece 10.67 25.62 3.10 870.85 6.28
Guatamala 3.01 46.05 0.87 289.71 1.48
Honduras 7.70 47.32 0.58 232.44 3.19
Iceland 1.27 34.03 3.08 1900.10 1.12
India 9.00 41.31 0.96 88.94 1.54
Ireland 11.34 31.16 4.19 1139.95 2.99
Italy 14.28 24.52 3.48 1390.00 3.54
Japan 21.10 27.01 1.91 1257.28 8.21
Korea 3.98 41.74 0.91 207.68 5.81
Luxembourg 10.35 21.80 3.73 2449.39 1.57
Malta 15.48 32.54 2.47 601.05 8.12
Norway 10.25 25.95 3.67 2231.03 3.62
Netherlands 14.65 24.71 3.25 1740.70 7.66
New Zealand 10.67 32.61 3.17 1487.52 1.76
Nicaragua 7.30 45.04 1.21 325.54 2.48
Panama 4.44 43.56 1.20 568.56 3.61
Paraguay 2.02 41.18 1.05 220.56 1.03
Peru 12.70 44.19 1.28 400.06 0.67
Philippines 12.78 46.26 1.12 152.01 2.00
Portugal 12.49 28.96 2.85 579.51 7.48
South Africa 11.14 31.94 2.28 651.11 2.19
South Rhodesia 13.30 31.92 1.52 250.96 2.00
Spain 11.77 27.74 2.87 768.79 4.35
Sweden 6.86 21.44 4.54 3299.49 3.01
Switzerland 14.13 23.49 3.73 2630.96 2.70
Turkey 5.13 43.42 1.08 389.66 2.96
Tunisia 2.81 46.12 1.21 249.87 1.13
United Kingdom 7.81 23.27 4.46 1813.93 2.01
United States 7.56 29.81 3.43 4001.89 2.45
Venezuela 9.22 46.40 0.90 813.39 0.53
Zambia 18.56 45.25 0.56 138.33 5.14
Jamaica 7.72 41.12 1.73 380.47 10.23
Uruguay 9.24 28.13 2.72 766.54 1.88
Libya 8.89 43.69 2.07 123.58 16.71
Malaysia 4.71 47.20 0.66 242.69 5.08
In this dataset sr represents savings ratio, pop15 represents
the percent of population under age 15, pop75 is the percent of
population over age 75, dpi is the real per-capita disposable income,
and ddpi is the percent growth rate of dpi. The most
commonly used graphical method for summarizing quantitative data is the
histogram. To construct a histogram, we first partition the data
values into a set of non-overlapping intervals and then obtain a frequency
table. A histogram is the barplot of the corresponding frequency data. Here
are histograms for savings ratio and disposable income.
In some applications, the proportions within the sub-intervals are of greater interest than the frequencies. In these cases a relative frequency histrogam can be used instead. In this case the vertical axis is re-scaled by dividing the frequencies by the total number of observations. The shape of a relative frequency histogram is unchanged; the only quantity that changes is the scale of the vertical axis.
There is no fixed number of sub-intervals that should be used. A large number of sub-intervals corresponds to less summarization of the data, and a small number of sub-intervals corresponds to more summarization.
When two or more variables are measured for each individual in the dataset, then we may be interested in the relationship between these variables. The type of graphical display we use depends on the types of the variables. We have already seen an example of a 2-dimensional barplot for the case in which both variables are categorical. If both variables are quantitative, then the basic graphical tool is the scatterplot. For example, here is a scatterplot of pop15 versus pop75.
The relationships among all 5 of the variables in this dataset can be displayed simultaneously by constructing pairwise scatterplots on the same graphic.
Note: we will defer until later in the course a discussion of numerical descriptions of these relationships.
