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

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.

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.

Explanation:

Analyze the level of measurement of the data

The data categories ("Research online and in store, buy in store", "Search and buy online", etc.) represent qualitative descriptions without any inherent numerical value, order, or ranking. Therefore, the data are at the nominal level of measurement.

Determine the calculation of the median

Because nominal data cannot be ordered or ranked, a middle value (median) cannot be determined. Thus, the median cannot be calculated because the data are at the nominal level of measurement.

Evaluate if the median represents the center

Since the data set is nominal and does not have a median, the median does not exist and cannot represent the center of the data.

Answer:

Question 1

• 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. (Correct answer)

Question 2

• 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.

<mcq-option>D. The median does not represent the center because it is not a data entry.</mcq-correct>

• E. The data set does not have a median. (Correct answer)