# Standard Deviation Calculator

The Standard Deviation Calculator can be used to calculate both the Population Standard Deviation, as well as the Sample Standard Deviation. Each value should be separated by a comma. Example is included below.

Enter Values (each value separated by comma):

## How to use the Standard Deviation Calculator

Let's review a simple example to demonstrate how to use the Standard Deviation Calculator, where:

• The data points to be entered into the calculator are: 2,7,15,4,8

To get the Standard Deviation, simply type/copy the above data points into the entry box, and then click on the Calculate Standard Deviation button:

You'll then get the the Population Standard Deviation of 4.445, and the Sample Standard Deviation of 4.970:

## How to Manually Calculate the Standard Deviation

You can use the following formula to calculate the Population Standard Deviation:

```                                                           [Σ(xi - μ)2]0.5
Population Standard Deviation (σ)  =      (N)0.5
```

Where:

Alternatively, you may use this formula to get the Sample Standard Deviation:

```                                                       [ Σ(xi - x̅)2 ]0.5
Sample Standard Deviation (s)  =      (n-1)0.5
```

Where:

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

## Calculation Example

Suppose that you have the following data points: 2,7,15,4,8.

Your goal is to calculate the:

• Population Standard Deviation (σ); and
• Sample Standard Deviation (s)

### Calculate the Population Standard Deviation

• μ = (2+7+15+4+8) / 5 = 7.2
• Σ(xi - μ)2 = (2-7.2)2 + (7-7.2)2 + (15-7.2)2 + (4-7.2)2 + (8-7.2)2 = 98.8
• N = 5
```                                                           [Σ(xi - μ)2]0.5          [98.8]0.5
Population Standard Deviation (σ)  =      (n)0.5     =   (5)0.5  =  4.445
```

You'll then get the Population Standard Deviation of 4.445.

### Calculate the Sample Standard Deviation

• x̅ = (2+7+15+4+8) / 5 = 7.2
• Σ(xi - x̅)2 = (2-7.2)2 + (7-7.2)2 + (15-7.2)2 + (4-7.2)2 + (8-7.2)2 = 98.8
• n = 5
```                                                       [ Σ(xi - x̅)2 ]0.5        [98.8]0.5
Sample Standard Deviation (s)  =      (n-1)0.5    =    (5-1)0.5  =  4.970
```

You'll now get the Sample Standard Deviation of 4.970.