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)  X^{2}  fx 



010  5  5  25  25  27  22  484 
1020  8  15  225  120  27  12  144 
2030  15  25  625  375  27  2  4 
3040  16  35  1225  560  27  8  64 
4050  6  45  2025  270  27  18  324 
 n = 






From actual mean:
Assumed mean method:
Where d=xA (A is assumed mean)
Method based on actual data
Variance:
It is square of the standard deviation
Standard deviation =