# Statistics Calculator: Standard Deviation

Use this calculator to compute the standard deviation from a set of numerical values.

Data is from: Population Sample

## Standard Deviation Calculator Instructions

This calculator computes the standard deviation from a data set:

Specify whether the data is for an entire population or from a sample. Enter your population or sample observed values in the box above. Values must be numeric and may be separated by commas, spaces or new-line. You may also copy and paste data into the text box. Press the "Submit Data" button to perform the computation. To clear the calculator and enter a new data set, press "Reset".

### What is the standard deviation

Standard deviation is the square root of the variance. It is one of the measures of dispersion, that is a measure of by how much the values in the data set are likely to differ from the mean

### Standard deviation formulas

This calculator uses the following formulas for calculating standard deviation:

The formula for the standard deviation of a sample is:

where n is the sample size and x-bar is the sample mean.

The formula for the standard deviation of an entire population is:

where N is the population size and μ is the population mean.