Question

Calculate the mean and S.D. for the following data :

$\begin{array}{cccccc}Expenditure\left(in\right):& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency:& 14& 13& 27& 21& 15\end{array}$

Answer 1

$\begin{array}{ccccccc}CI& f& x& u=(x-A)/h& fu& u^2& f{u}^2\\ 0-10& 14& 5& -2& -28& 4& 56\\ 10-20& 13& 15& -1& -13& 1& 13\\ 20-30& 27& 25& 0& 0& 0& 0\\ 30-40& 21& 35& 1& 21& 1& 21\\ 40-50& 15& 45& 2& 30& 4& 60\\ & 90& & & 10& & 150\end{array}$

Here, N= 90, A = 25, $\sum f_i{u}_i=10,\sum f_i{u}_i^2=150andh=10$

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

$\Rightarrow =\overline{x}=25+10\left(\frac{10}{90}\right)=26.11$

var (x) = $h^2[\frac{1}{N}\sum f_i{u}_i^2-{(\frac{1}{N}\sum f_i{u}_i)}^2]=100[\frac{150}{90}-{\left(\frac{10}{90}\right)}^2]=165.4$

$\therefore S.D.=\sqrt{var\left(x\right)}=\sqrt{165.4}=12.86$