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# Standard Deviation Examples

Below are few example problems on how to calculate standard deviation (SD). This standard deviation example questions can help you to calculate mean, variance, SD easily.

## Standard Deviation Example Problems

#### Example 1:

Let us consider a data sample : 10,13,7,9,6

###### Solution:

We can calculate the mean, variance and standard deviation of the given sample data using the given formula.

#### Formula :

###### Mean :
Mean = Sum of X values / N(Number of Values)
Variance = s2
###### Standard Deviation :

Substituting the values in the formula,

Number of Values, n = 5

Mean, M = (10 + 13 + 7 + 9 + 6) / 5 = 45 / 5 = 9 is the mean of the data set.

Standard Deviation, s = √∑(X-9)2 / (5 - 1) = √[(10 - 9)2 + (13 - 9)2 + (7 - 9)2 + (9 - 9)2 + (6 - 9)2] / 4 = √[12 + 42 + (-2)2 + 0 + -32] / 4 = √[1 + 16 + 4 + 9] / 4 = √[30 / 4] = √7.5 = 2.73861 Hence, the value of Sample Standard deviation is 2.73861.

Variance of the Sample = 2.738612 = 7.5 Hence, the value of Sample Variance is 7.5

#### Example 2:

Let us consider a population : 20,12,9,5,1

###### Solution:

We can calculate the mean, variance and standard deviation of the given population using the formula.

#### Formula :

Substituting the values in the formula,

Number of Values, n = 5

Mean, M = (20 + 12 + 9 + 5 + 1) / 5 = 47 / 5 = 9.4 is the mean of the population.

Standard Deviation, s = √∑(X - 9.4)2 / 5
= √[(20 - 9.4)2 + (12 - 9.4)2 + (9 - 9.4)2 + (5 - 9.4)2 + (1 - 9.4)2] / 5
= √[10.62 + (2.6)2 + (-0.4)2 + -4.42 + (-8.4)2] / 5
= √[112.36 + 6.76 +0.16 + (19.36) + 70.56] / 5
= √[209.2 / 5]
= √41.84
= 6.46838
Hence, the value of Population Standard deviation is 6.46838.

Variance of the Population = 6.468382 =41.84 Hence, the value of Sample Variance is 41.84