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

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

a. the mean cost is 43.7
(round to one decimal place as needed.)
b. there is no mean cost.

does the mean represent the center of the data?

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

Explanation:

Order the data set

Using the Median Calculation knowledge point
To find the median, we first arrange the 14 data values in ascending order:

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

Calculate the mean cost

Using the Mean Calculation knowledge point

$$
LATEXBLOCK0
$$

Rounded to one decimal place, the mean is \(43.7\).

Interpret the mean representation

Using the Measures of Central Tendency Interpretation knowledge point

$$ \text{The mean } 43.7 \text{ lies near the middle of the data range } [35, 47] \text{ and is not skewed by extreme outliers.} $$

Thus, the mean represents the center of the data.

Calculate the median cost

Using the Median Calculation knowledge point
Since \(N = 14\) is even, the median is the average of the 7th and 8th values:

$$
LATEXBLOCK1
$$

The median cost is \(44.0\) (or \(44\)).

Answer:

Question 1

• A. The mean cost is 43.7 (Correct answer)
• B. There is no mean cost.

Question 2

• A. The mean represents the center. (Correct answer)
• 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.

Question 3

• A. The median cost is 44 (Correct answer)
• B. There is no median cost.