To understand the distribution of data, it is important to find the variability or spread in the data which can be found using two statistical measures **Variance** and **Standard Deviation**.

## What is Standard Deviation?

Standard Deviation (**σ**) is the measure of dispersion or the scatter of the data when compared to its mean. Dispersion is the extent to which values in a distribution differ from the mean of the distribution.

**Low**standard deviation denotes that the values are clustered around the mean.**Hight**standard deviation denotes the more spread of the data, that values are far away from the mean.**Zero**standard deviation denotes that all the values lie at the mean.

## How is Standard Deviation Calculated?

Standard Deviation is calculated as the square root of variance.

#### Variance

Variance is the measure of variability in data i.e the spread of data from the mean. Higher the Variance, the more the spread in data.

Variance=

where

**xi**= value of current data

**n**= no of data points

** i**= iterator which moves from 1 to n

= mean

In the above formula, the distance from the mean is squared to get the positive value of output.

## Standard Deviation Formula

Standard Deviation is calculated by taking the square root of Variance.

Standard Deviation=

### 1. Population Standard Deviation

Population standard deviation is calculated using each individual in the population, hence it is a fixed value.

σ = √Σ(x_{i}– μ)^{2}/ N

where:

**Σ**: A symbol that means “sum”**x**: The i_{i}^{th}value in a dataset**μ**: The population mean**N**: The population size

### 2. Sample Standard Deviation

Sample standard deviation is calculated using the samples drawn from the population, hence it is not a fixed value but rather a statistic.

s = √Σ(x_{i}– x̄)^{2}/ (n – 1)

where:

**Σ**: A symbol that means “sum”**x**: The i_{i}^{th}value in a dataset**x̄**: The sample mean**n**: The sample size

## Difference between Standard Deviation and Variance

Standard Deviation |
Variance |

The square root of variance. | The average squared difference from the mean. |

It is expressed in the same unit of measurement as of dataset. | It is expressed in the squared unit of measurement as of the dataset. |