Question

the responses of a sample of 5204 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.
how purchases are made frequency
research online and in - store, buy in - store 2209
search and buy online 1123
search and buy in - store 820
research online and in - store, buy online 1052

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 data are at the nominal level of measurement.
d. the mean cannot be calculated because the sample size is too small.
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 not a data entry.
c. the mean does not represent the center because it is the greatest data entry.
d. the mean does not represent the center because it is the least data entry.
e. the data set does not have a mean.
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 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.

Explanation:

Step1: Identify data type

The data on how purchases are made (e.g., research online and in - store, buy in - store) is nominal data. Nominal data consists of categories without any numerical value or order.

Step2: Recall measure requirements

The mean requires numerical data for calculation (sum of values divided by number of values). Since nominal data has no numerical values, the mean cannot be calculated.

Step3: Recall median requirements

The median also requires data that can be ordered. Nominal data cannot be ordered in a meaningful numerical way, so the median cannot be calculated.

Step4: Recall mode

The mode is the most frequently occurring category. For nominal data, we can find the mode.

Answer:

1. C. The mean cannot be calculated because the data are at the nominal level of measurement.
2. E. The data set does not have a mean.
3. B. The median cannot be calculated because the data are at the nominal level of measurement.