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,

 how to calculate the standard deviation

 

 

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.

how to calculate the standard deviation

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

how to calculate the standard deviation

  • 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

how to calculate the standard deviation c

  • 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.