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 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 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.

Explanation:

Sort the data set

Using the Median Calculation knowledge point

$$ \text{Original data: } 47, 44, 35, 44, 47, 39, 47, 44, 42, 44, 47, 42, 46, 44 $$

$$ \text{Sorted data: } 35, 39, 42, 42, 44, 44, 44, 44, 44, 46, 47, 47, 47, 47 $$

Calculate the mean cost

Using the Mean Calculation knowledge point

$$ \sum x = 35 + 39 + 42 + 42 + 44 + 44 + 44 + 44 + 44 + 46 + 47 + 47 + 47 + 47 = 612 $$

$$ N = 14 $$

$$ \mu = \frac{612}{14} \approx 43.714 \approx 43.7 $$

Interpret the mean representation

Using the Measures of Central Tendency Interpretation knowledge point
The mean value of \(43.7\) lies near the middle of the sorted data range \([35, 47]\) and is not skewed by extreme outliers. Thus, the mean represents the center.

Calculate the median cost

Using the Median Calculation knowledge point

$$ N = 14 \quad (\text{even}) $$

$$ \text{Median} = \frac{x_{(7)} + x_{(8)}}{2} = \frac{44 + 44}{2} = 44 $$

Interpret the median representation

Using the Measures of Central Tendency Interpretation knowledge point
The median value of \(44\) lies in the middle of the sorted data set and represents the center of the data.

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.

Question 4

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