# Variance Calculator

Variance Calculator calculates the variance of the given set of numbers. In mathematics, variance helps us to measure the dispersion of values from the mean or the average. When we square the standard deviation, the variance is obtained.

## What is a Variance Calculator?

Variance Calculator is an online tool that helps to calculate the variance for an ungrouped data set. Variance is used to reflect the variability in the distribution with respect to the mean. To use this * variance calculator*, enter values inside the brackets, separated by a comma.

### Variance Calculator

## How to Use Variance Calculator?

Please follow the steps given below to find the variance using the online variance calculator:

**Step 1:**Go to Cuemath’s online variance calculator.**Step 2:**Enter the numbers separated by a comma within the brackets in the given input box of the variance calculator.**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 enter new values.

## How Does Variance Calculator Work?

There are two types of variance, namely, sample variance and population variance. To determine the population variance of ungrouped data, the steps are as follows:

**Step 1:**Determine the mean of the data set. This is denoted by \(\overline{x}\).**Step 2:**Now subtract the mean from each observation.**Step 3:**Square the values obtained in step 2.**Step 4:**Add all the squared values obtained in step 3.**Step 5:**Now divide this value by the total number of observations (n).

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

Mean or Average (\(\overline{x}\)) = (x_{1} + x_{2} + x_{3}...+ x_{n}) / n = \(\sum_{1}^{n}\frac{x_{i}}{n}\)

Where n = total number of terms, x_{1},_{ }x_{2},_{ }x_{3}, . . . , x_{n} = \(x_{i}\) = n different terms.

The variance can be given by the following formula:

Variance = \(\sum_{1}^{n}\frac{(x_{i} - \overline{x})^{2}}{n}\)

## Solved Examples on Variance

**Example 1:** Find the variance for the following set of data: {51, 38, 79, 46, 57} and verify it using the Variance Calculator.

**Solution:**

Given n = 5

Population variance = \(\sum_{1}^{n}\frac{(x_{i} - \overline{x})^{2}}{n}\)

Mean = (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 population variance is 193.052.

**Example 2:** Find the variance for the following set of observations: {7.2, 3.1, 8, 0, 4.7, 2} and verify it using the Variance Calculator.

**Solution:**

Given n = 6

Population variance = \(\sum_{1}^{n}\frac{(x_{i} - \overline{x})^{2}}{n}\)

Mean = (7.2 + 3.1 + 8 + 0 + 4.7 + 2) / 6 = 4.17

Variance = (7.2 − 4.17)^{2} + (3.1 − 4.17)^{2} + (8 − 4.17)^{2} + (0 − 4.17)^{2} + (4.7 − 4.17)^{2} + (2 − 4.17)^{2} / (6)

= 7.9

Therefore, the population variance is 7.9

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

- 1, 4.8, 6, 8, 2.89, 4.2, 15, 8.23
- 2, 1, 7, 5, 16, 4, 14, 25, 7

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