Standard deviation () is defined as the square root of the arithmetic mean of the square of the deviation of the values taken from mean. 

For an individual series

 

Example:

 

Marks	Frequency (f)	Mid value (x)	X2	fx
0-10	5	5	25	25	27	22	484
10-20	8	15	225	120	27	12	144
20-30	15	25	625	375	27	2	4
30-40	16	35	1225	560	27	8	64
40-50	6	45	2025	270	27	18	324
	n =

 

From actual mean:

 

Assumed mean method:

       Where d=x-A (A is assumed mean)

 

Method based on actual data

 

  

Variance:

It is square of the standard deviation

Standard deviation =

 

Download pdf file of Standard deviation and Variance