10. For questions 10-13, use the following data:
13 29 41 60 89 14 26 53 7 14
What is the arithmetic mean of the data? (Points: 5)
20
14
34.6
82
11. What is the range of the data? (Points: 5)
14
34.6
82
50
12. What is the variance of the data? (Points: 5)
231.04
616.64
685.16
1,197.16
13. What is the standard deviation of the data? (Points: 5)
0.2
26.18
24.83
34.61
To find the arithmetic mean of the data, you need to add up all the values and then divide by the total number of values.
For question 10, add up all the values: 13 + 29 + 41 + 60 + 89 + 14 + 26 + 53 + 7 + 14 = 356.
Then divide by the total number of values (which is 10): 356 / 10 = 35.6.
Therefore, the arithmetic mean of the data is 35.6. Since none of the given options match this value, it seems there might be an error in the given answer choices.
To find the range of the data, you need to subtract the smallest value from the largest value.
For question 11, the smallest value in the data is 7 and the largest value is 89.
Therefore, the range of the data is 89 - 7 = 82.
To find the variance of the data, you need to calculate the average of the squared differences between each data point and the mean.
For question 12, you can follow these steps:
1. Calculate the mean of the data (as found in question 10): 35.6.
2. Subtract the mean from each data point and square the result.
3. Find the average of the squared differences.
Using these steps, the calculation for each data point is as follows:
(13 - 35.6)^2 = 506.56
(29 - 35.6)^2 = 43.36
(41 - 35.6)^2 = 28.09
(60 - 35.6)^2 = 601
(89 - 35.6)^2 = 2580.84
(14 - 35.6)^2 = 470.44
(26 - 35.6)^2 = 92.16
(53 - 35.6)^2 = 303.61
(7 - 35.6)^2 = 822.44
(14 - 35.6)^2 = 470.44
Then, average the squared differences:
(506.56 + 43.36 + 28.09 + 601 + 2580.84 + 470.44 + 92.16 + 303.61 + 822.44 + 470.44) / 10 = 611.204
Therefore, the variance of the data is approximately 611.204.
To find the standard deviation of the data, you need to take the square root of the variance.
For question 13, the square root of 611.204 is approximately 24.73.
Therefore, the standard deviation of the data is approximately 24.73.