Learn How to Calculate Sample Population Variance – Tutorial

How to Calculate Sample Population Variance – Definition, Formula and Example

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.

Formula:
sample-variance-formula
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

xx - μ(x - μ)2
4-1.753.0625
82.255.0625
2-3.7514.0625
93.2510.5625
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

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Learn how to calculate the Sample Population Variance in this tutorial which is given with the definition, formula and example.

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