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 mean. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

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

Explanation:

Identify the level of measurement of the data

The data consists of qualitative categories representing how purchases are made (e.g., "Research online and in store, buy in store"). This represents the nominal level of measurement.

Determine if the mean can be calculated

Because the data are qualitative (nominal), numerical operations such as addition and division cannot be performed on the categories themselves. Therefore, the mean cannot be calculated.

Answer:

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