# Standard Deviation Calculator

Standard Deviation Calculator calculates the standard deviation of a given data from the mean. It helps us to know the variation of the given set of values. For example, a set of values has three numbers 3,5,7. Its mean would be (3+5+7)/3 = 5. The calculator will calculate how much is the deviation of these numbers from the mean number 5.

## What is a Standard Deviation Calculator?

Standard Deviation Calculator is an online tool that helps to calculate the variation from the mean. It helps to calculate the standard deviation in a few seconds. To use this * standard deviation calculator*, enter values inside the bracket, separated by a comma.

### Standard Deviation Calculator

## How to Use Standard Deviation Calculator?

Please follow the steps to find the standard deviation for the given values using online standard deviation calculator:

**Step 1:**Go to Cuemath’s online standard deviation calculator.**Step 2**: Enter the numbers in the input box.**Step 3:**Click on the "Calculate" button to find the standard deviation.**Step 4:**Click on the "Reset" button to clear the fields and enter new values.

## How Standard Deviation Calculator Works?

**Standard deviation** is commonly denoted as SD or σ, and it tells about the value that how much it has deviated from the mean value.

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

where xi 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) = (x1 + x2 + x3...+ xn) / n , where n = total number of terms, x1, x2, x3, . . . , xn = Different n terms

## Solved Example on Standard Deviation

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

**Solution:**

Given N =5

Standard deviation = √(∑(xi - 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

**Example 2:** Find the standard deviation for the following set of data: {28,18,69,35,54}

**Solution:**

Given N = 5

Mean (x) = ( 28 + 18 + 69 + 35 + 54 ) / 5 = 40.8

Standard deviation = √(28 - 40.8)^{2} + (18 - 40.8)^{2} + (69 - 40.8)^{2} + (35 - 40.8)^{2} + (54 - 40.8)^{2} / (5-1)

= 20.54

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

- 21,14,16,8,2,4,15,8
- 25,1,7,15,6,14,14,25,7

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