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 σ²

Formula:
Population Variance = Σ(X_i- X)²/ N
Where,
X_i= I^th 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.

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