© John Wiley & Sons, Inc.

FIGURE 9-1: A frequency bar chart (a) and pie chart (b).

Summarizing Numerical Data

Summarizing a numerical variable isn’t as simple as summarizing a categorical variable. The summary

statistics for a numerical variable should convey how the individual values of that variable are

distributed across your sample in a concise and meaningful way. These summary statistics should give

you some idea of the shape of the true distribution of that variable in the population from which you

draw your sample (read Chapter 3 and Chapter 6 to refresh your memory about sampling). That true

population distribution can have almost any shape, including the typical shapes shown in Figure 9-2:

normal, skewed, pointy-topped, and bimodal (two-peaked).

© John Wiley & Sons, Inc.

FIGURE 9-2: Four different shapes of distributions: normal (a), skewed (b), pointy-topped (c), and bimodal (two-peaked) (d).

How can you convey a visual picture of what the true distribution may look like by using just a few

summary numbers? By reporting values of measures of some important characteristics of these

distributions, so that the reader can infer the shape. This is similar to learning that one Olympic ice