Calculation of Arithmetic Mean & Standard Deviation

by

Short Method from Assumed Mean

             
             
Assumed Mean(AM)- Interval -      
Class interval          

SCORE

Mid-point(x)

Frequency(f)

x'

fx'

fx'2
c: ci: Mean: c2 - SD :    
             
             

Formulae:

Arithmetic Mean = Assumed Mean + ci; where c = fx' / (sum of the frequencies=N ), i= no. of entries in a class interval;

Standard Deviation = i*√ [(Σ fx'2 / N) - c2]

Take Assumed Mean as the mid value corresponding to maximum frequency. In general, any value with the range of values can

 be taken as Assumed Mean.