Question

the tuition and fees (in thousands of dollars) for the top 14 universities in a recent year are listed below. find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a measure does not represent the center of the data, explain why.

47, 44, 35, 44, 47, 39, 47
44, 42, 44, 47, 42, 46, 44

a. the mean represents the center.
b. the mean does not represent the center because it is the smallest data value.
c. the mean does not represent the center because it is not a data value.
d. the mean does not represent the center because it is the largest data value.
e. there is no mean cost.

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

a. the median cost is 44.
(round to one decimal place as needed.)
b. there is no median cost.

does the median represent the center of the data?

a. the median represents the center.
b. the median does not represent the center because it is not a data value.
c. the median does not represent the center because it is the largest data value.
d. the median does not represent the center because it is the smallest data value.
e. there is no median cost.

find the mode of the costs. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the mode(s) of the costs is (are) .
(round to one decimal place as needed. use a comma to separate answers as needed.)
b. there is no mode.

Explanation:

Organize the data set

Using the Measures of Central Tendency knowledge point
The given data set consists of the tuition and fees (in thousands of dollars) for the top 14 universities:

$$ 47, 44, 35, 44, 47, 39, 47, 44, 42, 44, 47, 42, 46, 44 $$

Sorting the 14 values in ascending order:

$$ 35, 39, 42, 42, 44, 44, 44, 44, 44, 46, 47, 47, 47, 47 $$

Find the mode of the data set

We count the frequency of each unique value in the sorted list:

• \(35\): occurs 1 time
• \(39\): occurs 1 time
• \(42\): occurs 2 times
• \(44\): occurs 5 times
• \(46\): occurs 1 time
• \(47\): occurs 4 times

The value \(44\) has the highest frequency of occurrence (5 times). Therefore, the mode of the data set is \(44\).

Answer:

• A. The mode(s) of the costs is (are) 44 (Correct answer)
• B. There is no mode.