# Standard Deviation Calculator

'Cuemath's Standard Deviation Calculator' is an online tool that helps to calculate the standard deviation for the given numbers.

## What is a Standard Deviation Calculator?

Cuemath's online Standard Deviation Calculator helps you to calculate the standard deviation for the given numbers in a few seconds.

Note: Enter values inside the bracket, separated by a comma

## How to Use Standard Deviation Calculator?

Please follow the steps below to find the standard deviation for the given numbers:

**Step 1:**Enter the numbers separated by a comma in the given input box.**Step 2:**Click on the**"Calculate"**button to find the standard deviation for the given numbers.**Step 3:**Click on the**"Reset"**button to clear the fields and find the standard deviation for the different numbers.

## How to Find Standard Deviation Calculator?

**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 = √(∑(x_{i} - x)^{2} / (N - 1)),

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

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(x) = (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 standard deviation for the following set of data: {51,38,79,46,57}

**Solution:**

Given N =5

Standard deviation = √(∑(x_{i} - x)^{2} / (N - 1))

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

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

= 15.5

Therefore, the standard deviation is 15.5.

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

a) 21,14,16,8,2,4,15,8

b) 25,1,7,15,6,14,14,25,7