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How to use variance Formula and calculate variance :


Step-1:Determine all possible outcomes

This calculator calculates the variance from set of values. First step it uses is to take square of all the values available in the entire population:

X X2
25 625
35 1225
45 2025
55 3025

Step-1: Calculate the Mean

$$\sum x\;=\;160$$

Take the square of answer and divide that value by size of population.

$$\frac{(\sum x)^2}{N}\;=\;\frac{160^2}{4}\;=$$

$$\frac{25600} {4}\;=\;6400$$

Then calculate the sum of all the square values, ∑x2

$$\sum x^2\;=\; 6900$$


$$\sum x^2\;-\;\frac{(\sum x)^2}{N}\;=$$


Step-13: Calculate Variance

For Variance, divide the answer with size of population,

$$σ^2\;=\;\frac{\sum x^2\;-\;\frac{(\sum x)^2}{N}}{N}\;=$$

$$\frac{6340} {4}=7576$$

So the Variance is 1585