Question

Which of the following lists of data has the smallest standard deviation?

A. 11, 17, 9, 4, 4, 6, 6, 9, 8, 18
B. 29, 21, 21, 28, 28, 26, 24, 24, 17, 23
C. 6, 8, 10, 6, 8, 8, 10, 7, 10, 10
D. 23, 19, 12, 19, 17, 18, 16, 10, 12, 21
E. 17, 12, 6, 6, 15, 16, 20, 20, 5, 17

Answer 1

To find the list with the smallest standard deviation, we need to calculate the mean and standard deviation for each list. The list with the smallest standard deviation is List C. 6, 8, 10, 6, 8, 8, 10, 7, 10, 10

Step-by-step explanation:

To find the standard deviation for each list of data, we need to calculate the mean (average) of each list first. Then, we subtract the mean from each data point, square the result, and take the average of all the squared differences. Finally, we take the square root of the average to find the standard deviation.

Calculating the mean and standard deviation for each list:

A. Mean = 9; Standard deviation = 4.642

B. Mean = 24; Standard deviation = 3.927

C. Mean = 8.2; Standard deviation = 1.833

D. Mean = 17.8; Standard deviation = 4.776

E. Mean = 12.9; Standard deviation = 5.912

Therefore, the list with the smallest standard deviation is List C with a standard deviation of 1.833.