Question

The following data values represent a sample. What is the variance of the

sample? X = 8. Use the information in the table to help you.
х
12
9
11
5
3
(x; - x)²
16
1
9
9
25

Answer 1

The variance of the data is 15.

σ² = 15

Explanation:

The mean is given as

X = 8

х | (x - X) | (x - X) ²

12 | 4 | 16

9 | 1 | 1

11 | 3 | 9

5 | -3 | 9

3 | -5 | 25

The variance is given by

`\sigma^2 = (1)/(n-1) \sum (x - X)^2`

`\sigma^2 = (1)/(5 - 1) (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = (1)/(4) ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = (1)/(4) (60) \\\\\sigma^2 = 15`

Therefore, the variance of the data is 15.