# Standard Deviation Calculator

In the calculator below, enter the series of numbers whose standard deviation you want to know, one number per line or with a space between the numbers and press the calculate button.

## What is the standard deviation?

It is a measure that uses the distribution of numbers in a series around the average of that series to summarize the spread of the data values.

## How is standard deviation calculated?

Firstly, the arithmetic mean of the data in the series is found. Then the difference between each data and the arithmetic mean of the series is found. Each of the differences found is squared and the resulting numbers are summed. This sum is divided by the number of data minus 1 and the square root of the section is found. When it is desired to find the standard deviation of the population, in the last step, instead of missing the number of data 1, division is performed.

## What is variance?

It is a measure of the change in values in a series relative to the average.

## How is variance calculated?

It is calculated by finding the average of all the numbers in a series and the average of the squares of their differences.

## For what purposes can this calculator be used?

Knowing the standard deviation value for a given series number and understanding this concept means understanding how much this series is spreading around an average. The large standard deviation indicates that the data points are spread farther than the average; being smaller indicates that they are more closely grouped around the average.

## What other information can I learn about the series of numbers I entered?

You can calculate the largest and smallest element of the series, the arithmetic mean, variance, standard deviation, and standard deviation and variance of the population.