# Standard Deviation Calculator - Calculatorall.com

This is our standard deviation calculator that will allow you to calculate standard deviation, mean variance, and sum for a given set of numbers.
In statistics, the Standard deviation is usually denoted by σ and it measures dispersion or variation between the values of a data set. Lower standard deviation means that the data points are closer. On the contrary, higher value of standard deviation means there are wide ranging values in the data set. And just like other concepts of mathematics, the applications for the standard deviation can be many. Besides expressing the variability of population, Standard Deviation can be used for measuring the statistical results like margin of error. In such situations, standard deviation an also be termed as standard error of mean. Our standard deviation calculator here can be used for measuring population standard deviation as well as sample standard deviation.

 Please provide numbers separated by comma to calculate. 10,2,38,23,38,23,21
Population Standard Deviation

It is used when it is possible to measure an entire population and is calculated by taking square root of variance of any given set of data. For populations where it is possible to sample all the members, use the equation given below for finding that population's standard deviation.

Where
xi is individual value
μ is mean/expected value
N is total number of values

Sample Standard Deviation

Sometimes you have to study populations where it isn't possible for you to sample all the members of the population. So, in such cases, the above mentioned equation needs some modification allowing you to measure standard deviation using some random sample. So, here you can use sample standard deviation which is denoted by the letter s. However, it should be kept in mind that sample standard deviation can be calculated using different equations. The equation that we have shown below is for "corrected sample standard deviation". It is obtained after modification of population standard deviation and uses sample size to serve as size of population. Here it is:

Where xi is one sample value
͞x is sample mean
N is sample size

How It Works

Our standard deviation calculator here works quite simply. All you have to do is to enter the values separated by a comma and hit the calculate button. The calculator takes over from there and calculates the results for you. You get everything with just a single click. Including Sample Standard deviation and its variance, population standard deviation and its variance, total numbers and their sum and the mean of the numbers you have entered. So, if you are looking for all these values, use our calculator to get the accurate results.