Question

The weight of coffee in 70 jars is shown in the following table :

$\begin{array}{ccccccc}\text{Weight (in grams)}:& 200-201& 201-202& 202-203& 203-204& 204-205& 205-206\\ \text{Frequency}:& 13& 27& 18& 10& 1& 1\end{array}$

Determine the variance and standard deviation of the above distribution.

Answer 1

$\begin{array}{cccccc}CF& f_i& x_i& d_i=x_i-\overline{X}& f_i{d}_i& f_i{d}_i^2\\ 200-201& 13& 200.5& -2& -26& 52\\ 201-202& 27& 201.5& -1& -27& 27\\ 202-203& 18& 202.5& 0& 0& 0\\ 203-204& 10& 203.5& 1& 10& 10\\ 204-205& 1& 204.5& 2& 2& 4\\ 205-206& 1& 205.5& 3& 3& 9\\ & \sum f_i=70& & & \sum f_i{d}_i=-38& \sum f_i{d}_i^2=102\end{array}$

${\sigma }^2=\frac{\sum f_i{d}_i^2}{\sum f_i}={\left(\frac{\sum f_i{d}_i}{\sum f_i}\right)}^2=\frac{102}{70}-{\left(\frac{-38}{70}\right)}^2$

Now, = 1.4571-0.2916 = 1.1655

$\sigma =\sqrt{1.1655}=1.08g$