Question

Consider the following distribution of daily wages of 50 workers of a factory.

$\begin{array}{cccccc}\text{Daily wages (in Rs)}& 100-120& 120-140& 140-160& 160-180& 180-200\\ \text{Number of workers}& 12& 14& 8& 6& 10\end{array}$

Find the mean daily wages of the workers of the factory by using an appropriate method.

Answer 1

Let us find the class mark for each interval by using the relation:

$x_i=\frac{\text{Upper class limit + lower class limit}}{2}$

Class size (h) of this data = 20
Now taking 150 as assured mean (a) we may calculate di, $u_i$ and $f_i{u}_i$ as following:

$\begin{array}{cccccc}\text{Daily wages (in Rs)}& \text{Number of workers}\left(f_i\right)& x_i& d_i=x_i-150& u_i=\frac{x_i-150}{h}& f_i{u}_i\\ 100-20& 12& 110& -40& -2& -24\\ 120-140& 14& 130& -20& -1& -14\\ 140-160& 8& 150& 0& 0& 0\\ 160-180& 6& 170& 20& 1& 6\\ 180-200& 10& 190& 40& 2& 20\\ Total& 50& & & & -12\end{array}$

From the table we may observe that:

$h=20$

$a=150$

$\sum f_i=50f_i{u}_i=-12Mean\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)hMean=150+\left(\frac{-12}{50}\right)20=150-\frac{24}{5}=150-4.8=145.2$

So, mean daily wages of the workers of the factory is Rs.145.20