Discrete Standard Deviation
For calculating standard deviation in discrete series any of the following methods may be applied
(1) Actual mean method.
(2) Assumed mean method.
(3) Step deviation method.
(a) Actual mean methods when this method is applied deviations are taken from the actual mea we find (X-X) and denote these deviations by x. These deviations are then squared and multiplied by the respective frequencies. The following formula is applied:
s = v S fx2 /N where x = (X – X)
However in practice this method is rarely used because if the actual mean is in fractions the calculations take a lot of time.
(b) Assumed mean method when this method is used the following for mule is applied
S = v {fd2 / N – ({ fd/N)2 where d = (x – A)
Steps
Take the deviations of the items form an assumed mean and denote there deviation by d.
Multiply these deviations by the respective frequencies and obtain the total { fd.
Obtain the squares of the deviations calculate d2. Multiply the squared deviations by the respective frequencies an obtain the total {fd2.
Substitute the value in the above formula