What is the standard deviation of 1,3,4,4,6,7,8,9,9,9

Question

The mean of this data set is 6.

Answer 1

To calculate the standard deviation, first take the mean (average). In this case it's done for you (6).

For each number, subtract  the mean, then square this value.

Take the mean of these squared differences.

Given:

1, 3, 4, 4, 6, 7, 8, 9, 9, 9  and mean = 6

1 - 6 = -5, (-5)^2 = 25

3 - 6 = -3, (-3)^2 = 9

4 - 6 = -2, (-2)^2 = 4

6 - 6 = 0, 0^2 = 0

7 - 6 = 1, 1^2 = 1

8 - 6 = 2, 2^2 = 4

9 - 6 = 3, 3^2 = 9

now take the mean:

[25 + 9 + 4 + 4 + 0 + 1 + 4 + 9 + 9 + 9]/10 = 74/10 = 7.4

The standard deviation is 7.4