How do i find the standard deviation from this set of numbers?

Question

3,6,6,8,11,11,14,15,18,18,22,24

Answer 1

The data set is 3 ,6 ,6 ,8 ,11 ,11 ,14 ,15 ,18 ,18 , 22 , 24

Calculate the standard deviation by using following formula

Where

S is standard deviation of sample.

  = each value in the data set.

= Mean of all values in the data set.

N = number of values in the data set.

Step - 1) Find the mean

Step - 2) Then for each number subtract mean and square the result.

(3 - 13)² = (10)² = 100

(6 - 13)² = (- 7)² = 49

(6 - 13)² = (-7)² = 49

(8 - 13)² = (-5)² = 25

(11 - 13)² = (-2)² = 4

(11 - 13)² = (- 2)² = 4

(14 - 13)² = (1)² = 1

(15 - 13)² = (2)² = 4

(18 - 13)² = (5)² = 25

(18 - 13)² = (5)² = 25

(22 - 13)² = (9)² = 81

(24 - 13)² = (11)² = 121

Step - 3) Find the mean of squared difference.

We are calculating sample standard deviation, so instead of dividing by N, we will divided by N - 1.

= 488/11

= 44.36

Standard deviation .