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.

39 43 43 43 43 35 41
41 43 47 46 46 46 41

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
(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 largest 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 smallest 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.

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.

39 43 43 43 43 35 41
41 43 47 46 46 46 41

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
(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 largest 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 smallest 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.

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Mean Calculation", "Median Calculation", "Measures of Center" ], "current_concepts": [ "Mean Calculation", "Median Calculation", "Measures of Center" ] } ## Calculate the mean cost $$ \begin{aligned} \text{Data: } & 39, 43, 43, 43, 43, 35, 41, 41, 43, 47, 46, 46, 46, 41 \ \sum x &= 39 + 43 + 43 + 43 + 43 + 35 + 41 + 41 + 43 + 47 + 46 + 46 + 46 + 41 = 594 \ N &= 14 \ \mu &= \frac{594}{14} \approx 42.42857 \end{aligned} $$ ## Determine if the mean represents the center $$ \begin{aligned} &\text{The mean is } 42.4 \text{ thousand dollars.} \ &\text{The data values range from } 35 \text{ to } 47. \ &\text{There are no extreme outliers pulling the mean significantly away from the middle.} \ &\text{Therefore, the mean represents the center.} \end{aligned} $$ ## Calculate the median cost $$ \begin{aligned} \text{Sorted Data: } & 35, 39, 41, 41, 41, 43, 43, 43, 43, 43, 46, 46, 46, 47 \ \text{Median Position: } & \frac{14 + 1}{2} = 7.5 \ \text{Median} &= \frac{x_{(7)} + x_{(8)}}{2} = \frac{43 + 43}{2} = 43.0 \end{aligned} $$ ## Question 1 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 42.4 B. There is no mean cost. ## Question 2 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 largest 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 smallest data value.

E. There is no mean cost. ## Question 3 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 43.0

B. There is no median cost.

{ "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Measures of Center" ] }

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Explanation:

Calculate the mean cost

Determine if the mean represents the center

Calculate the median cost

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Question 1

Question 2

Question 3