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

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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 in store
research online and in store, buy online
search and buy online
research online and in store, buy in store
the data set does not have a mode.

Explanation:

Determine the level of measurement of the data

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

Analyze the existence of the median

Because nominal data is qualitative and cannot be ordered or ranked, mathematical operations like finding a middle value are not possible. Therefore, the data set does not have a median.

Identify the mode of the data

The mode is the category with the highest frequency. Comparing the frequencies:

• 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

The category "Search and buy in store" has the highest frequency of 2255.

Answer:

Question 1

• 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. (Correct answer)

Question 2

• Search and buy in store (Correct answer)
• Research online and in store, buy online
• Search and buy online
• Research online and in store, buy in store
• The data set does not have a mode.