Question

the responses of a sample of 5204 shoppers who were asked how their purchases are made are shown in the table. find the mean, the median, and the mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why.

a. the median is (round to one decimal place as needed.)
b. the median cannot be calculated because there is an even number of data entries.
c. the median cannot be calculated because the data are at the nominal level of measurement.
d. the median cannot be calculated because the sample size is too small.

does the median represent the center of the data? choose the correct answer below
a. the median represents the center of the data set.
b. the median does not represent the center because it is the least data entry.
c. the median does not represent the center because it is the greatest data entry
d. the median does not represent the center because it is not a data entry.
e. the data set does not have a median.

find the mode. choose the correct answer below.
search and buy online
research online and in store, buy online
research online and in store, buy in store
search and buy in store
the data set does not have a mode.

Explanation:

Step1: Recall measure - level concept

Median is applicable for ordinal, interval, and ratio - level data. Nominal - level data (categories like "Research online and in store, buy in store") have no inherent order, so median can't be calculated.

Step2: Determine mode

Mode is the most frequently occurring category. We need to find the category with the highest frequency among the purchase - making methods.

Answer:

For median: C. The median cannot be calculated because the data are at the nominal level of measurement.
For does median represent center: E. The data set does not have a median.
For mode: We need the frequency values to determine the mode. Since the frequency values in the provided image are not clearly readable (the numbers are blurry), we cannot give a definite answer for the mode part based on the current information. If we assume the frequencies are as follows (from the best - guess of the blurry image: 2226, 1123, 420, 1037), the mode is "Research online and in store, buy in store" as it has the highest frequency. But this is a speculation based on unclear data.