# How to Calculate The Standard Deviation

Introduction to how to calculate the standard deviation:

A common measure of dispersion which is preferred in most circumstances in statistics is the standard deviation.

Definition of standard deviation:

The positive square root of the mean of the squared deviatios of the data from the mean is called the standard deviation. It is denoted by `sigma` .

## Formula for how to calculate the standard deviation

The standard deviation `sigma` of a frequency distribution is calculated using the formula,

## Methods for how to calculate the standard deviation

The following are the methods used for calculating standard deviation:

• Direct method
• Assumed mean method
• Actual mean method
• Step deviation method

## Methods of calculating standard deviation:

Direct method:

In this method, the standard deviation is calculated directly using the formula.

This formula is used to find the standard deviation in direct method.

• Find `sum` x and  `sum` x2
• Substitute the values of  `sum` x and  `sum` x2  and the number of data n in the formula

## Methods of calculating standard deviation:

Assumed mean method:

When the data is large or the mean is not an integer we use assumed mean method to calculate the standard deviation.

• Choose one of the items nearer to the middle value in the data say A as the assumed mean.
• Calculate deviation d = x - A for each value of the series and find  `sum` d ,  `sum` d2 .
• Substitute `sum` d ,  `sum` d2 and n in the formula and calculate the standard deviation.

The formula for standard deviation is,

## Methods of calculating standard deviation:

Actual mean method:

The formula used in this method is

• Calculate the mean

• Calculate the deviation and find `sum` d2

• Substitute `sum` d2 , n in the formula  and calculate the standard deviation.

## Methods of calculating standard deviation:

Step Deviation Method:

The formula for standard deviation in this method is

• Choose one of the middle values in the series as the assumed mean A.
• Calculate d = x - A for each value of the series.
• Find c , where c is the common factor of all d.
• Find `sum` d′, `sum` d′2, c and n in the formula and calculate the standard deviation.