Question

Find the coefficient of variation for the following data :

$\begin{array}{ccccccc}\text{Size (in cms ):}& 10-15& 15-20& 20-25& 25-30& 30-35& 35-40\\ \text{No of items}:& 2& 8& 20& 35& 20& 15\end{array}$

Answer 1

$\begin{array}{ccccccc}CI& f& x& u=(x-A)lh& fu& u^2& f{u}^2\\ 10-15& 2& 12.5& -2& -4& 4& 8\\ 15-20& 8& 17.5& -1& -8& 1& 8\\ 20-25& 20& 22.5& 0& 0& 0& 0\\ 25-30& 35& 27.5& 1& 35& 1& 35\\ 30-35& 20& 32.5& 2& 40& 4& 80\\ 35-40& 15& 37.5& 3& 45& 9& 135\\ & 100& & & 108& & 266\end{array}$

Here , N = 100, A = 22.5, $\sum f_i{u}_i=108,\sum f_i{u}_i^2=266$ and h = 10

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

$\Rightarrow \overline{x}=22.5+5\left(\frac{108}{100}\right)=27.90$

$var\left(x\right)=h^2[\frac{1}{N}\sum f_i{u}_i^2-{\left(\frac{1}{N}sum{f}_i{u}_i\right)}^2]=25[\frac{266}{100}-{\left(\frac{108}{100}\right)}^2]=37.34$

$\therefore S.D=\sqrt{var\left(x\right)}=\sqrt{37.34}=6.11$

coefficient of variation = $\frac{S.D}{\overline{X_1}}\times =\frac{6.11}{27.90}\times =21.9$