Learn How to Calculate Sample Population Variance – Tutorial

Definition:

Sample variance is a measure of the spread of or dispersion within a set of sample data.The sample variance is the square of the sample standard deviation σ. It is an unbiased estimator of the square of the population standard deviation, which is also called the variance of the population.

Example :

Given,

x : 4, 8, 2, 9

To Find,

Sample Variance σ²

Solution:

Step 1 :

Find the value of μ from the given values 4,8,2,9. μ = (4+8+2+9) / 4 μ = 5.75

Step 2 :

Let us now calculate the value of (x - μ)² from the μ value = 5.75

Step 3 :

Find the ∑(x - μ)² with the values of (x - μ)² ∑(x - μ)² = 3.0625+5.0625+14.0625+10.5625 ∑(x - μ)² = 32.75 Now, substitute the value of ∑(x - μ)² and ‘n’ in the formula of Sample Variance σ² σ² = 32.75 / 4 σ² = 8.1875