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 \boxed{}. (type an integer or decimal rounded to one decimal place as needed.) b. the data set does not have a mean.

Explanation:

Step1: List the data values

The data set is: 8, 10, 11, 11, 8, 7, 7, 7, 9, 7, 7, 7, 8.

Step2: Calculate the sum of the data

First, count the number of values, \( n = 13 \).
Now sum the values:
\( 8 + 10 + 11 + 11 + 8 + 7 + 7 + 7 + 9 + 7 + 7 + 7 + 8 \)
Let's group the numbers:

• Number of 7s: Let's count. The 7s are at positions 6,7,8,10,11,12. Wait, let's list all: 7,7,7,7,7,7 (that's 6 times).
• Number of 8s: Positions 1,5,13. So 3 times. 8*3 = 24.
• Number of 9s: 1 time. 9*1 = 9.
• Number of 10s: 1 time. 10*1 = 10.
• Number of 11s: 2 times. 11*2 = 22.

Now sum: \( 7\times6 + 8\times3 + 9 + 10 + 11\times2 \)
\( 42 + 24 + 9 + 10 + 22 \)
\( 42+24 = 66 \); \( 66 + 9 = 75 \); \( 75 + 10 = 85 \); \( 85 + 22 = 107 \). Wait, no, wait: 76=42, 83=24, 9=9, 10=10, 11*2=22. Then 42+24=66, 66+9=75, 75+10=85, 85+22=107? Wait, but let's add again manually:
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. Yes, sum is 107.

Step3: Calculate the mean

Mean \( \bar{x} = \frac{\text{Sum of data}}{n} \), where \( n = 13 \).
So \( \bar{x} = \frac{107}{13} \approx 8.2307... \), rounded to one decimal place is 8.2. Wait, wait, no: 107 divided by 13. Let's do the division: 13*8 = 104, 107 - 104 = 3, so 8 + 3/13 ≈ 8.2307, which is approximately 8.2 when rounded to one decimal place. Wait, but let's check the sum again. Wait, the data points: 8,10,11,11,8,7,7,7,9,7,7,7,8. Let's count the number of each:

• 7: Let's see, positions 6,7,8,10,11,12. That's 6 times. 7*6=42.
• 8: positions 1,5,13. 3 times. 8*3=24.
• 9: position 9. 1 time. 9*1=9.
• 10: position 2. 1 time. 10*1=10.
• 11: positions 3,4. 2 times. 11*2=22.

Now sum: 42 + 24 = 66; 66 + 9 = 75; 75 + 10 = 85; 85 + 22 = 107. Correct. Then 107 /13 ≈ 8.23, so to one decimal place, 8.2. Wait, but maybe I made a mistake in counting the data points. Let's count the number of data points: 8,10,11,11,8,7,7,7,9,7,7,7,8. Let's count: 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). So 13 data points. Correct. So sum is 107. Mean is 107/13 ≈ 8.2 (rounded to one decimal place).

Wait, but let's recalculate the 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. Yes, correct. So 107 divided by 13 is approximately 8.23, so 8.2 when rounded to one decimal place.

Answer:

The mean is \(\boxed{8.2}\) (rounded to one decimal place). So the correct choice is A, and the mean is 8.2.