Question

For which of the following would it be inappropriate to display the data with a single pie chart?

(a) The distribution of car colors for vehicles purchased in the last month

(b) The distribution of unemployment percentages for each of the 50 states

(c) The distribution of favorite sport for a sample of 30 middle school students (d) The distribution of shoe type worn by shoppers at a local mall

(e) The distribution of presidential candidate preferences for voters in a state

Short answer

Option (b) is correct.

Step-by-step solution

Step 1. Given information.

From the given options in the questions, we have to choose the correct option for the given statement which says for which option it would be inappropriate to display the data with a single pie chart.

Step 2. Explanation for the correct option.

If any subject appears in exactly one of the different categories and the total of all categories (expressed in percentages) must equal 100 percent, a pie chart is appropriate.

(a) A pie chart for the distribution of car colours is appropriate, given that each car has precisely one colour (or that we use its primary colour).

(b) Constructing a pie chart for the distribution is inappropriate since the total unemployment percentages for the 50 states will not be 100%.

For example, if each of the 50 states has a 10% unemployment rate (which could happen in the event of a severe economic crisis), the overall unemployment rate for the 50 states is 500%, thus we can't make a pie chart in this situation.

(c) A pie chart for the distribution of preferred sports is appropriate, assuming that each middle school student has only one favourite sport (or only answers with one favourite sport).

(d) A pie chart showing the distribution of shoe type is reasonable, assuming that each shopper is wearing a different shoe type.

(e) For the distribution of presidential candidate choices, a pie chart is appropriate, given that each person has precisely one preference (or is undecided).

Therefore, the correct option is (b) "The distribution of unemployment percentages for each of the 50 states".