Question

the responses of a sample of 5338 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.

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$$\begin{tabular}{|l|c|} \\hline \\textbf{how purchases are made} & \\textbf{frequency, f} \\\\ \\hline research online and in store, buy in store & 863 \\\\ search and buy online & 1050 \\\\ search and buy in store & 2255 \\\\ research online and in store, buy online & 1170 \\\\ \\hline \\end{tabular}$$

a. the mean represents the center of the data set.
b. the mean does not represent the center because it is the least data entry.
c. the mean does not represent the center because it is not a data entry.
d. the mean does not represent the center because it is the greatest data entry.
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 \\\\
(round to one decimal place as needed.)
b. the median cannot be calculated because the sample size is too small.
c. the median cannot be calculated because there is an even number of data entries.
d. the median cannot be calculated because the data are at the nominal level of measurement.

Explanation:

Analyze the level of measurement of the data

The data represents qualitative categories describing how purchases are made (e.g., "Research online and in store, buy in store"). This is nominal level data because the categories cannot be ordered, ranked, or measured numerically.

Determine the calculation of the mean

Because the data is nominal (qualitative), numerical calculations like the mean cannot be performed. Therefore, the data set does not have a mean.

Determine the calculation of the median

Because the data is nominal, the entries cannot be ordered or ranked from smallest to largest. Therefore, the median cannot be calculated because the data are at the nominal level of measurement.

Answer:

Question 1

• A. The mean represents the center of the data set.
• B. The mean does not represent the center because it is the least data entry.
• C. The mean does not represent the center because it is not a data entry.
• D. The mean does not represent the center because it is the greatest data entry.
• E. The data set does not have a mean. (Correct answer)

Question 2

• A. The median is [ ].
• B. The median cannot be calculated because the sample size is too small.
• C. The median cannot be calculated because there is an even number of data entries.
• D. The median cannot be calculated because the data are at the nominal level of measurement. (Correct answer)