# How to Find Population Variance?

How do you calculate the Population Variance?

## Population Variance Calculation

Variance measure how far a data is from the mean of the given data. The variance of a whole population can be termed as population variance. It is the square of the standard deviation. It is represented using the symbol Ïƒ2 Formula:
Population Variance = Î£(Xi- X)2/ N
Where,
Xi= Ith Element of Sample
X = Mean of N elements
N = Number of Elements Step 1: Let us consider the set of data : 6, 8, 1, 2, 10, 15 Step 2: Substituting the values in the mean formula,
Mean (X) = (6+8+1+2+10+15) / 6
= 42 / 6
X = 7 Step 3: Substitute the mean and other values in the formula,
Perform the (Xi-X) operation for all values of i (from 1 to n)
Population Variance
= [(7-6)2+ (7-8)2+ (7 - 10)2+ (7- 2)2+ (7- 1)2+ (7- 15)2]/ (6)
= [(1)2+ (-1)2+ (-3)2+ (5)2+(6)2+ (-8)2/ (6)
= (1 + 1 + 9 + 25 + 36 + 64) / 6
= 136 / 6
= 22.66
Hence, the population variance is 22.66 You can calculate the variance of a given set in a population using Population Variance Calculator.