Chapter 2, Problem 134CP

Mode but not median and mean The previous exercise showed how to find the mean and median when a categorical variable has ordered categories. A categorical scale that does not have ordered categories (such as choice of religious affiliation or choice of major in college) is called a nominal scale. For such a variable, the mode (or modal category) applies, but not the mean or median. Explain why.

2.133 Political conservatism and liberalism Where do Americans tend to fall on the conservative–liberal political spectrum? The General Social Survey asks, “I’m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal, point 1, to extremely conservative, point 7. Where would you place yourself on this scale?” The table shows the seven-point scale and the distribution of 1933 responses for a survey conducted in 2008.

This is a categorical scale with ordered categories, called an ordinal scale. Ordinal scales are often treated in a quantitative manner by assigning scores to the categories and then using numerical summaries such as the mean and standard deviation.

1. a. Using the scores shown in the table, the mean for these data equals 4.11. Show that you get the mean by multiplying each score by the frequency it occurred, summing up these values and then dividing the sum by the total number of observations.
2. b. Identify the mode (or modal category).
3. c. In which category does the median fall? Why?