The following **Variance Calculator** can be used to derive both the *Population Variance*, and the *Sample Variance*. Simply enter your values in the entry box. Each value should be separated by a comma. Example is included below.

## How to use the Variance Calculator

Let's say that you have the following values:

**21, 12, 16, 20, 26**

The goal is to get both the *Population Variance*, and the *Sample Variance.*

To start, enter the values in the Variance Calculator as follows:

Next, click on the **Calculate Variance** button, and you'll get the Population Variance of **22.4**, as well as the Sample Variance of **28**:

You may also get the Standard Deviation for your data by using the Standard Deviation Calculator.

## How to Manually Derive the Variance

You may use the following formula to derive the **Population Variance**:

` [Σ(xi - μ)`^{2}]

Population Variance = N

Where:

- μ = Mean (average of all data points)
- xi = Value of each data point
- N = Total number of data points

Alternatively, you can use this formula to get the **Sample Variance**:

` Σ(xi - x̅)`^{2}

Sample Variance = n-1

Where:

- x̅ = Sample Mean (average of all data points)
- xi = Value of each data point
- n = Sample size

## Calculation Example

Let's say that you want to derive the Population Variance, and the Sample Variance, for the following data points:

**21, 12, 16, 20, 26 **

To start, let's compute the Population Variance:

- μ = (21+12+16+20+26) / 5 =
**19** - Σ(xi - μ)
^{2}= (21-19)^{2}+ (12-19)^{2}+ (16-19)^{2}+ (20-19)^{2}+ (26-19)^{2}=**112** - N =
**5**

` [Σ(xi - μ)`^{2}] 112

Population Variance = N = 5 = 22.4

Therefore, the Population Variance is **22.4**.

Finally, let's compute the Sample Variance:

- x̅ = (21+12+16+20+26) / 5 =
**19** - Σ(xi - x̅)
^{2}= (21-19)^{2}+ (12-19)^{2}+ (16-19)^{2}+ (20-19)^{2}+ (26-19)^{2}=**112** - n =
**5**

Σ(xi - x̅)^{2}112

Sample Variance = n-1 = 5-1 = 28

You'll now get the Sample Variance of **28**.