Question

The monthly salary brackets of the employees of a company (in Rs) and the corresponding number of employees is tabulated below. Find M.D(M)

$\begin{array}{cc}Salary\left(Rs/Month\right)& Numberofemployees\\ 0-20000& 20\\ 20000-40000& 25\\ 40000-60000& 15\\ 60000-80000& 12\\ 80000-100000& 8\end{array}$

• A. Rs 12800
• B. Rs 14100
• C. Rs 18600
• D. Rs 21500

Answer 1

The correct option is D Rs 21500

$\begin{array}{ccc}Class& Frequency& Cumulativefrequency\\ 0-20000& 20& 20\\ 20000-40000& 25& 45\\ 40000-60000& 15& 60\\ 60000-80000& 12& 72\\ 80000-100000& 8& 80\end{array}$

Here, N = 80
$\therefore \frac{N}{2}=40$

Hence, median class is 20000-40000

$Median=L+\frac{\frac{N}{2}-c.f}{f}\times h=20000+\frac{40-20}{25}\times 20000=Rs36000$

Deviations from the median are tabulated below

$\begin{array}{cccc}X\left(classmidpoint\right)& F& D=|X-M|& FD\\ 10000& 20& 26000& 520000\\ 30000& 25& 6000& 150000\\ 50000& 15& 14000& 210000\\ 70000& 12& 34000& 408000\\ 90000& 8& 54000& 432000\\ & \sum F=80& & \sum FD=1720000\end{array}$

$M.D\left(M\right)=\frac{1720000}{80}=Rs21500$