Question

the responses of a sample of 524 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.
a. the median is
(round to one decimal place as needed.)
b. the median cannot be calculated because there is an even number of data entries.
c. the median cannot be calculated because the data are at the nominal level of measurement.
d. the median cannot be calculated because the sample size is too small.
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.
find the mode. choose the correct answer below.
a. search and buy online
b. research online and in - store, buy online
c. research online and in - store, buy in - store
d. search and buy in - store
e. the data set does not have a mode.

Explanation:

Step1: Recall measure - type relationship

Median requires ordinal or interval - ratio data. The data on how purchases are made is nominal (categories like search and buy online, etc. with no order). So, median cannot be calculated.

Step2: Analyze mode concept

Mode is the most frequently occurring category. In a frequency - distribution of nominal data, we can find the mode.

Answer:

1. C. The median cannot be calculated because the data are at the nominal level of measurement.
2. E. The data set does not have a median.
3. We need the frequency data to determine the mode. If we assume the highest - frequency category is the mode, without seeing the frequencies we cannot choose from the given options. But if we had the frequencies, the mode would be the category with the highest frequency among "Search and buy online", "Research online and in - store, buy online", "Research online and in - store, buy in - store", "Search and buy in - store".