Question

Yuri computes the mean and standard deviation for the sample data set 12, 14, 9, and 21. He finds the mean is 14. His steps for finding the standard deviation are below. What is the first error he made in computing the standard deviation?

A. Yuri failed to find the difference between each data point and the mean.
B. Yuri divided by n instead of n -1.
C. Yuri did not subtract 9 - 14 correctly.
D. Yuri failed to square -2 correctly.

Answer 1

Option B.

Explanation:

Consider the below figure attached with this question.

Formula for standard deviation of a sample:

`s=\sqrt{\frac{\sum (x-\overline{x})^2}{n-1}}`

where, n is sample size and
`\overline{x}` is sample mean.

The sample data set is 12, 14, 9, and 21.

The mean is 14.

So, the sample standard deviation is

`s=\sqrt{((12-14)^2+(14-14)^2+(9-14)^2+(21-14)^2)/(4-1)}`

According to Yuri,

`s=\sqrt{((12-14)^2+(14-14)^2+(9-14)^2+(21-14)^2)/(4)}`

Yuri divides the sum of square of difference between each data point and the mean by n instead of n -1.

Therefore, the correct option is B.