Standard deviation for grouped data:

It is computed by following formula.

                                                         [3^rd Form]

here is A.M., x is the size of item, and f is corresponding frequency in case of discrete series.

But when mean has a fractional value, then following formula can be applied to calculate S.D.

                                                  [4^th Form]

here     d = x - A, A = is the assumed mean, n = Sf = total frequency.

Standard deviation in continuous series:

Direct Method. The standard deviation in case of continuous series can be obtained by following formula.

                                                         [5^th Form]

here x = mid-value,  = A.M., f = frequency, n = total frequency.

Combined Standard Deviation:

Assume that s₁ and s₂ be the S.D. of the 2 groups containing n₁ and n₂ items respectively. Let ₁ and ₂ be their respective A.M. Let x and s be A.M. and S.D. of combined group respectively. Then

Variance  

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