# Variance Calculator

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.

Enter Values (each value separated by comma):

## 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:

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.