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 \\\\
(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.

does the mean represent the center of the data? choose the correct answer below.
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.

Explanation:

Determine the level of measurement of the data

The data represent qualitative categories of how purchases are made (e.g., "Research online and in store, buy in store"). This is nominal data because the categories are labels without any inherent numerical value or mathematical order.

Evaluate the calculation of the mean

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

Determine if the mean represents the center

Since the mean cannot be calculated for nominal data, the data set does not have a mean.

Answer:

Question 1

• (A) The mean is .
• (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)

Question 2

• (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.

<mcq-option>(D) The mean does not represent the center because it is the greatest data entry.</mcq-correct>

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