Question

The hourly wages of 30 workers are given below. Find the mean deviation about the mean of the wages.
$\begin{array}{cc}Wage\left(inRs\right)& Numberofworkers\\ 10& 5\\ 20& 9\\ 30& 9\\ 40& 4\\ 50& 3\end{array}$

• A. 8.75
• B. 9.87
• C. 11.4
• D. 12.33

Answer 1

The correct option is B 9.87

To calculate the mean using assumed mean method, choose 30 as the assumed mean

$\begin{array}{cccc}X& F& d=X-A& Fd\\ 10& 5& -20& -100\\ 20& 9& -10& -90\\ 30(=A)& 9& 0& 0\\ 40& 4& 10& 40\\ 50& 3& 20& 60\\ & \sum F=30& & \sum Fd=-90\end{array}$

$Meanwage=A+\frac{\sum Fd}{\sum F}=30+\frac{-90}{30}=Rs27$

Deviations from the mean are tabulated below

$\begin{array}{cccc}X& F& D=|X-\overline{X}|& FD\\ 10& 5& 17& 85\\ 20& 9& 7& 63\\ 30& 9& 3& 27\\ 40& 4& 13& 52\\ 50& 3& 23& 69\\ & \sum F=30& & \sum FD=296\end{array}$

$M.D\left(\overline{x}\right)=\frac{296}{30}=9.87$