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 :
Variance = s2
Standard Deviation :
Standard Deviation Formula

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.

Population Standard Deviation :

Formula :

Population Standard Deviation 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

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