How to Find Population Standard Deviation?

How to Calculate Standard Deviation (SD) of a Population ?

SD of a Population Calculation

In statistics, a population is an entire group from which a sample can be selected. This online tutorial will help you to learn how to find the Standard deviation (SD) of a population.How To Calculate Population Standard Deviation
Formula :
SD of Population =√Σ (X -M)2/ n
Where,
X = Elements
M = Mean
n = Number of ElementsPopulation Standard Deviation Formula
Step 1:
Let us consider the data of a population as :3,7,1,18,20
We can calculate the mean as : (3+7+1+18+20 ) / 5
= 49 / 5
Mean = 9.8
Sample Standard Deviation Step1
Step 2:
Substituting the below values in the formula of population SD,
SD of Population = √{[(3-9.8)2+ (7-9.8)2+ (1-9.8)2+ (18-9.8)2+ (20-9.8)2] / 5}
= √{[(-6.8)2+ (-2.8)2+ (-8.8)2+ (8.2)2+ (10.2)2] / 5}
= √{46.24 + 7.84 + 77.44 + 67.24 + 104.04 / 5}
= √(302.8 / 5)
= √(60.56)
= 7.78
Sd Of Population Calculation Step2


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