methods of calculation of standard deviation

Question

Methods  of calculation of standard deviation

a.Calculation of Standard  Deviation  - Individual Series: There  are two methods of calculating standard  deviation in an individual  observation or series

a.Deviation Taken from Actual Mean: This method is adopted when  the mean  is a whole  number of an even number . the   followings are the steps.

1.Find out the  actual  mean  of the series (x¯ ) .

2.Find out  the deviation of each  value  from the mean ( X - x¯)

3.Square the deviations and  take the total  of squared devotions∑ X².

4. Divide the total (∑X²) by the number  of observations. The square  root  of the  quotient is standard deviation. Thus  apply the  following  formula:

                               = √∑X²/ N  or √ ∑ (X- x¯ )/ N