# Variance Calculator

## How does Variance Calculator work?

• Select the population or sample variance
• Input the comma-separated values of the data set.
• Hit The Calculate Button.
• Use the Reset button to calculate new values.

## Other Calculators

Variance calculator finds the variance of sample and population data values with steps. The sample variance calculator also provides the standard deviation, mean, and sum of squares.

## What is a variance?

In statistics, the variance is the measure of dispersion i.e., measure the spread of data values from the expected value. It is the expectation of the squared deviation of a random variable from its sample or population mean.

It is denoted by s2 and σ2 for sample and population data respectively.

## Variance formula

The formula for the sample variance is: The formula for the population variance is: ## How to calculate the variance?

Below are a few examples of variance solved by our mean and variance calculator.

Example 1: For sample variance

Find the variance of the given sample data.

2, 4, 7, 12, 15

Solution

Step 1: Calculate the sample mean of the given data.

Sample mean = x̅ = Σx/n

Sample mean = x̅ = [2 + 4 + 7 + 12 + 15]/5

Mean = x̅ = 40/5

Mean = x̅ = 8

Step 2: Now measure the dispersion and squares of deviation.

 Data values (x) xi - x̅ (xi - x̅)2 2 2 – 8 = -6 (-6)2 = 36 4 4 – 8 = -4 (-4)2 = 16 7 7 – 8 = -1 (-1)2 = 1 12 12 – 8 = 4 (4)2 = 16 15 15 – 8 = 7 (7)2 = 49

Step 3: Find the summation of the squared deviations.

Σ(xi - x̅)2 = 36 + 16 + 1 + 16 + 49

Σ(xi - x̅)2 =  118

Step 4: Now divide the sum of squares by n-1.

Σ(xi - x̅)2/n-1 = 118/5-1

Σ(xi - x̅)2 / n-1 = 118/4

Σ(xi - x̅)2 / n-1 = 29.5

Example 2: For population variance

Find the variance of the given population data.

1, 14, 19, 25, 26, 35

Solution

Step 1: Calculate the population mean of the given data.

Population mean = µ = Σx/n

= [1 + 14 + 19 + 25 + 26 + 35]/6

= 120/6

= 20

Step 2: Now measure the dispersion and squares of deviation.

 Data values (x) xi - µ (xi - µ)2 1 1 – 20 = -19 (-19)2 = 361 14 14 – 20 = -6 (-6)2 = 36 19 19 – 20 = 1 (1)2 = 1 25 25 – 20 = 5 (5)2 = 25 26 26 – 20 = 6 (6)2 = 36 35 35 – 20 = 15 (15)2 = 225

Step 3: Find the summation of the squared deviations.

Σ(xi - µ)2 = 361 + 36 + 1 + 25 + 36 + 225

Σ(xi - µ)2 =  684

Step 4: Now divide the sum of squares by n.

Σ(xi - µ)2/n = 684/6

Σ(xi - µ)2/n = 136.8

## References

Wikimedia Foundation. (2022, June 20). What is a variance? Wikipedia.