## Coefficient of variation for grouped data

Coefficient of variation is an absolute measure of variation and is used for the comparison of variability between two or more frequency distribution.

Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution.

## Formula

Coefficient of variation is given by

### $CV =\dfrac{s_x}{\overline{x}}\times 100$

where,

• $\overline{x} =\dfrac{1}{N}\sum_{i=1}^{n}f_ix_i$ is the sample mean of $X$,
• $N$ total number of observations,
• $s_x=\sqrt{V(x)}$ is the sample standard deviation of $X$,
• $s_x^2=V(x)=\dfrac{1}{N-1}\bigg(\sum_{i=1}^{n}f_ix_i^2 -\dfrac{\big(\sum_{i=1}^n f_ix_i\big)^2}{N}\bigg)$ is the sample variance of $X$