# What is the formula for standard deviation of grouped data?

Jan 13, 2017

${s}^{2} = \frac{{\sum}_{i = 1}^{i = n} {f}_{i} {x}_{i}^{2} - {\left({\sum}_{i = 1}^{i = n} {f}_{i} {x}_{i}\right)}^{2} / n}{n - 1}$

#### Explanation:

Let the mid points of classes of grouped data be ${x}_{1} , {x}_{2} , \ldots \ldots \ldots . {x}_{n}$

and their respective frequencies be ${f}_{1} , {f}_{2} , \ldots \ldots \ldots . {f}_{n}$

Then Standard Deviation $s$ is given by

${s}^{2} = \frac{{\sum}_{i = 1}^{i = n} {f}_{i} {x}_{i}^{2} - {\left({\sum}_{i = 1}^{i = n} {f}_{i} {x}_{i}\right)}^{2} / n}{n - 1}$