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.
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.
political view frequency
liberal 164
moderate 116
conservative 120

Explanation:

Step1: Identify the mode

The mode is the value with the highest frequency. Given frequencies: Liberal - 164, Moderate - 116, Conservative - 120. Since 164 is the highest frequency, the mode is the political - view corresponding to it.

Step2: Analyze mean and median

The data is categorical (political views: liberal, moderate, conservative). Mean is not appropriate for categorical data as it requires numerical values for calculation. Median for categorical data is not well - defined in a straightforward way as there is no natural ordering for calculating the middle value in the sense of numerical data.

Answer:

a. C. The mode is liberal.
b. It would not be appropriate to use either the mean or the median as a measure of center. The data is categorical (political views), and the mean requires numerical values for calculation, while the median is not well - defined for categorical data in a simple manner.