# Variance Calculator

Variance measures variability from the average or mean. It is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set.

## What is a Variance Calculator?

'Cuemath's Variance Calculator' is an online tool that helps to calculate the variance for the given numbers. Cuemath's online Variance Calculator helps you to calculate the variance for the given numbers in a few seconds.

## How to Use Variance Calculator?

Please follow the steps below to find the variance for the given numbers:

**Step 1:**Choose a drop-down list to find for sample and population variance**Step 2:**Enter the numbers separated by a comma in the given input box.**Step 3:**Click on the**"Calculate"**button to find the variance for the given numbers.**Step 4:**Click on the**"Reset"**button to clear the fields and find the variance for the different numbers.

## How to Find Variance?

**Variance (σ ^{2})** is the squared variation of values (X

_{i}) of a random variable (X) from its mean (μ) for ungrouped data. There are two types of variances:

1. Sample variance 2. Population variance

**Sample variance(σ ^{2}) = ∑(x_{i} - μ )^{2} / (N - 1)**

**Population variance(σ ^{2}) = ∑(x_{i} - μ )^{2} / (N)**

Where x_{i} is individual values in the sample, and μ is the mean or an average of the sample, N is the number of terms in the sample.

**Standard deviation** is** **commonly denoted as SD, and it tells about the value that how much it has deviated from the mean value.

**Standard deviation(σ) = √(∑(x _{i} - μ)^{2} / (N - 1))**

The** **mean value** **or average of a given data is defined as the sum of all observations divided by the number of observations. The mean is calculated using the formula:

**Mean or Average(μ) = (x _{1} + x_{2} + x_{3}...+ x_{n}) / n **

Where n = total number of terms, x_{1},_{ }x_{2},_{ }x_{3}, . . . , x_{n} = Different n terms

**Solved Example:**

Find the variance for the following set of data: {51,38,79,46,57}?

**Solution:**

Given N =5

For sample variance,

Sample variance(σ^{2}) = ∑(x_{i} - x)^{2} / (N - 1)

Mean(μ) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2

Variance = (51 − 54.2)^{2} + (38 − 54.2)^{2} + (79 − 54.2)^{2} + (46 − 54.2)^{2} + (57 − 54.2)^{2} / (5 - 1)

= 965.26 / 4

= 241.315

For population variance,

Population variance(σ^{2}) = ∑(x_{i} - x)^{2} / (N)

Mean(μ) = 51 + 38 + 79 + 46 + 57 / 5 = 54.2

Variance = (51 − 54.2)^{2} + (38 − 54.2)^{2} + (79 − 54.2)^{2} + (46 − 54.2)^{2} + (57 − 54.2)^{2} / (5)

= 965.26 / 5

= 193.052

Therefore, the sample variance is 241.315 and the population variance is 193.052.

Similarly, you can try the calculator to find the variance for the following:

- 1, 4, 6, 8, 2, 4, 15, 8
- 2, 1, 7, 5, 16, 4, 14, 25, 7