Question

in 2000, for a certain region, 45.9% of incoming college freshman characterized their political views as liberal, 27.2% as moderate, and 26.9% as conservative. for the current year, a random sample of 400 incoming college freshman yielded the frequency distribution for political views shown below.

a. determine the mode of the data using the given frequency distribution.
b. decide whether it would be appropriate to use either the mean or the median as a measure of center. explain your answer.

political view frequency
liberal 164
moderate 116
conservative 120

a. choose the correct answer below. select all that apply.

□ a. the mode is conservative.
□ b. the mode is moderate.
☑ c. the mode is liberal.
□ d. there is no mode.

b. would it be appropriate to use either the mean or the median as a measure of center?

○ a. the median would be an appropriate measure of center because it is not strongly affected by the relatively large gap between the smallest and largest frequencies.
○ b. the mean would be an appropriate measure of center because the political views of freshman in the sample is very similar to the percentages of all freshman.
○ c. since the data is qualitative, neither the mean nor the median can be used as a measure of center.
○ d. either the mean or the median would be an appropriate measure of center since they are approximately the same.

Explanation:

Step1: Identify the mode

The mode is the value that appears most frequently. Given frequencies: Liberal - 164, Moderate - 116, Conservative - 120. Since 164 (Liberal) is the highest frequency, the mode is liberal.

Step2: Analyze measure - of - center appropriateness

Political views (Liberal, Moderate, Conservative) are qualitative data. Mean and median are measures of central tendency for quantitative data. For qualitative data, these measures are not applicable.

Answer:

a. C. The mode is liberal.
b. C. Since the data is qualitative, neither the mean nor the median can be used as a measure of center.