Question

What is the formula for standard deviation of grouped data?

Answer 1

`s^2=(sum_(i=1)^(i=n)f_ix_i^2-(sum_(i=1)^(i=n)f_ix_i)^2/n)/(n-1)`

Explanation:

Let the mid points of classes of grouped data be `x_1,x_2,..........x_n`

and their respective frequencies be `f_1,f_2,..........f_n`

Then Standard Deviation `s` is given by

`s^2=(sum_(i=1)^(i=n)f_ix_i^2-(sum_(i=1)^(i=n)f_ix_i)^2/n)/(n-1)`