Question

the number of credits being taken by a sample of 13 full - time college students are listed below. find the mean, median, and mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why. 8 10 11 11 8 7 7 7 9 7 7 7 8... find the mean. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mean is 8.2. (type an integer or decimal rounded to one decimal place as needed.) b. the data set does not have a mean. 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 the largest data value. d. the mean does not represent the center because it is not a data value. e. the data set does not have a mean.

Explanation:

Part 1: Find the Mean

Step 1: List the data values

The data set is: \( 8, 10, 11, 11, 8, 7, 7, 7, 9, 7, 7, 7, 8 \) (13 values).

Step 2: Sum the data values

Calculate the total sum:
\( 8 + 10 + 11 + 11 + 8 + 7 + 7 + 7 + 9 + 7 + 7 + 7 + 8 \)
Break it down:

• Number of \( 7 \)s: \( 6 \) (sum: \( 6 \times 7 = 42 \))
• Number of \( 8 \)s: \( 3 \) (sum: \( 3 \times 8 = 24 \))
• Number of \( 9 \)s: \( 1 \) (sum: \( 9 \))
• Number of \( 10 \)s: \( 1 \) (sum: \( 10 \))
• Number of \( 11 \)s: \( 2 \) (sum: \( 2 \times 11 = 22 \))

Total sum: \( 42 + 24 + 9 + 10 + 22 = 107 \)? Wait, no—wait, let’s recalculate:

Wait, original data: Let’s count again. The data is: \( 8, 10, 11, 11, 8, 7, 7, 7, 9, 7, 7, 7, 8 \). Let’s list all 13:

1. 8
2. 10
3. 11
4. 11
5. 8
6. 7
7. 7
8. 7
9. 9
10. 7
11. 7
12. 7
13. 8

Now sum:
\( 8 + 10 = 18 \); \( 18 + 11 = 29 \); \( 29 + 11 = 40 \); \( 40 + 8 = 48 \); \( 48 + 7 = 55 \); \( 55 + 7 = 62 \); \( 62 + 7 = 69 \); \( 69 + 9 = 78 \); \( 78 + 7 = 85 \); \( 85 + 7 = 92 \); \( 92 + 7 = 99 \); \( 99 + 8 = 107 \). Wait, but the problem says the mean is 8.2? Wait, no—wait, 13 values. Let’s divide 107 by 13: \( \frac{107}{13} \approx 8.23 \), rounded to one decimal is 8.2. So the mean is \( \approx 8.2 \).

Part 2: Does the mean represent the center?

The mean is a measure of central tendency (center) of the data, as it is the average value. It is calculated from all data points, so it represents the center.

Answer:

A. The mean represents the center.

Final Answers:

• Mean: \( \boldsymbol{8.2} \)
• Does the mean represent the center? \( \boldsymbol{A} \)