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 $X$