# Standard Deviation Calculator

To Calculate Mean, Variance, Standard deviation :
Enter all the numbers separated by comma :
Mean (Average) :
Variance :
Standard deviation :

Standard Deviation Calculator is a free online tool that displays mean, variance, and standard deviation for the given set of data. BYJU’S online standard deviation calculator tool makes the calculation faster, and it displays the standard deviation in a fraction of seconds.

## How to Use the Standard Deviation Calculator?

The procedure to use the standard deviation calculator is as follows:

Step 1: Enter the numbers separated by a comma in the respective input field

Step 2: Now click the button “Solve” to get the SD

Step 3: Finally, the mean, variance, and standard deviation for the given set of data will be displayed in the output field

### What is Meant by Standard Deviation?

Standard Deviation is the measure of dispersion that can be found by how much the values in the given set of data are likely to differ from the mean. The symbol used to denote the standard deviation is σ. Variance and standard deviation both depend on the mean of a given set of numbers. Calculating these set of parameters depends on whether the given set is a sample or the population.

Variance and Standard Deviation of a Population Formula:

The population standard deviation is used to measure the variability of data in the population. The Variance is denoted as σ2 and Standard Deviation as σ and the formula of the population are given by:

$$\begin{array}{l}\large \sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\left ( x_{i}-\mu \right )^{2}}\\ \large \sigma^{2} = \frac{1}{N}\sum_{i=1}^{N}\left ( x_{i}-\mu \right )^{2}\end{array}$$

Where:
σ = population standard deviation
σ2 = population variance
x1, …, xN = the population data set
μ = mean of the population data set
N = size of the population data set

Variance and Standard Deviation of a Sample:
The sample standard deviation is an estimate of a population standard deviation which is based on a given sample. The variance is denoted as s2 and standard deviation as s and the formula for sample standard deviation are given by:

$$\begin{array}{l}\large s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left ( x_{i}-\overline{x} \right )^{2}}\\ \large s^{2}=\frac{1}{n-1}\sum_{i=1}^{n}\left ( x_{i}-\overline{x} \right )^{2}\end{array}$$

Where:
s = sample standard deviation
s2 = sample variance
x1, …, xn = the sample data set
x̄ = mean value of the sample data set
n = size of the sample data set