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
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Range = highest score-lowest score
I'll let you do the calculations.
To find the arithmetic mean, or average, of the data, you need to add up all the numbers and divide by the total count.
For question 10, we add up the data:
13 + 29 + 41 + 60 + 89 + 14 + 26 + 53 + 7 + 14 = 356
Next, we divide the sum by the number of data points which is 10:
356 / 10 = 35.6
Therefore, the arithmetic mean of the data is 34.6.
To find the range, you need to find the difference between the highest and lowest values in the data.
For question 11, the highest value is 89 and the lowest value is 7.
So the range of the data is 89 - 7 = 82.
For question 12, to find the variance, you need to calculate the average of the squared deviations from the mean.
First, find the mean which is 34.6 as we calculated earlier.
Next, subtract the mean from each data point and square the result:
(13 - 34.6)^2, (29 - 34.6)^2, (41 - 34.6)^2, (60 - 34.6)^2, (89 - 34.6)^2, (14 - 34.6)^2, (26 - 34.6)^2, (53 - 34.6)^2, (7 - 34.6)^2, (14 - 34.6)^2
Then, find the average of these squared deviations:
(13 - 34.6)^2 = 457.96, (29 - 34.6)^2 = 31.36, (41 - 34.6)^2 = 40.96, (60 - 34.6)^2 = 648.36, (89 - 34.6)^2 = 2952.16, (14 - 34.6)^2 = 428.36, (26 - 34.6)^2 = 74.76, (53 - 34.6)^2 = 333.16, (7 - 34.6)^2 = 720.36, (14 - 34.6)^2 = 428.36
The sum of these squared deviations is 6180.32.
Finally, divide this sum by the number of data points which is 10:
6180.32 / 10 = 618.032
Therefore, the variance of the data is 618.032.
For question 13, the standard deviation is the square root of the variance.
Taking the square root of the variance we calculated earlier:
sqrt(618.032) = 24.83
Therefore, the standard deviation of the data is 24.83.