Question

Calculate coefficient of variation from the following data :

$\begin{array}{ccccccc}\text{Income (in Rs):}& 1000-1700& 1700-2400& 2400-3100& 3100-3800& 3800-4500& 4500-5200\\ \text{No. of families}:& 12& 18& 20& 25& 35& 10\end{array}$

Answer 1

$\begin{array}{ccccccc}CI& f& x& u=(x-A)lh& fu& u^2& f{u}^2\\ 1000-1700& 12& 1350& -2& -24& 4& 48\\ 1700-2400& 18& 2050& -1& -18& 1& 18\\ 2400-3100& 20& 2750& 0& 0& 0& 0\\ 3100-3800& 25& 3450& 1& 25& 1& 25\\ 3800-4500& 35& 4150& 2& 70& 4& 140\\ 4500-5200& 10& 4850& 3& 30& 9& 90\\ & 120& & & 83& & 321\end{array}$

Here, N = 120, A = 2750, $\sum f_i{u}_i=83,\sum f_i{u}_i^2=321$ h = 700

$\therefore$ Mean = $\overline{x}=A+h(\frac{1}{N}\sum f_i{u}_i)$

$\Rightarrow \overline{x}=2750+700\left(\frac{83}{120}\right)=3234.17$

$var\left(x\right)=h^2[\frac{1}{N}\sum f_i{u}_i^2-{(\frac{1}{N}\sum f_i{u}_i)}^2]=49000[\frac{321}{120}-{\left(\frac{83}{120}\right)}^2]=1076332.64$

$\therefore S.D=\sqrt{var\left(x\right)}=\sqrt{1076332.64}=1037.46$

Coefficient of variation = $\frac{S.D}{\overline{x_1}}\times 100=\frac{1037.46}{3234.17}\times 100=32.08$