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:

$ s =\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2$

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


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

$ \sigma =\sqrt{\frac{1}{N} \sum_{i=1}^N (x_i-\mu)^2$

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