Question

the class levels of 32 students in a physics course are shown below. find the mean, median, and mode of the data, if possible. if any measure cannot be found, explain why. freshman: 3 sophomore: 11 junior: 10 senior: 8 use the mean to answer the question of the mean. a. the mean represents the center. b. the mean does not represent the center because it is not a data value. c. the mean does not represent the center because it is the largest data value. d. the mean does not represent the center because it is the smallest data value. e. the data set does not have a mean. find the median. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the median is (type an integer or decimal rounded to one decimal place as needed.) b. the median cannot be calculated because there are too many sophomores. c. the median cannot be calculated because the sample size is too small. d. the median cannot be calculated because the data are at the nominal level of measurement. does the median represent the center of the data? a. the median represents the center. b. the median does not represent the center because it is the largest data value. c. the median does not represent the center because it is not a data value. d. the median does not represent the center because it is the smallest data value. e. the data set does not have a median.

Explanation:

Step1: Recall mean - definition

Mean is calculated as $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. But class - levels (Freshman, Sophomore, Junior, Senior) are nominal data. We cannot perform arithmetic operations on nominal data. So, the data set does not have a mean.

Step2: Recall median - definition

Median is the middle - value when data is ordered. Nominal data cannot be ordered in a meaningful numerical way. So, the median cannot be calculated because the data are at the nominal level of measurement.

Answer:

For the question about the mean: E. The data set does not have a mean.
For the question about the median: D. The median cannot be calculated because the data are at the nominal level of measurement.
For the question about whether the median represents the center: E. The data set does not have a median.