Question

Find the coefficient of mean deviation about median for the following cumulative frequency distribution:

$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

• A. 0.187
• B. 0.203
• C. 0.215
• D. 0.224

Answer 1

The correct option is A

0.187

Here, the sum of frequencies, n = 40, which is even.
So, the median terms will be the $\frac{n}{2}th$ and the $(\frac{n}{2}+1)th$ observations, i.e. the 20th and the 21st observations.
Both the 20th and the 21st observations are 54.
So, the median term, M= 54.

Deviations from the median are tabulated below

$\begin{array}{cccc}X& F& D=|X-M|& FD\\ 22& 1& 32& 32\\ 34& 2& 20& 40\\ 39& 2& 15& 30\\ 45& 8& 9& 72\\ 54& 8& 0& 0\\ 56& 9& 2& 18\\ 68& 4& 14& 56\\ 78& 4& 24& 96\\ 84& 2& 30& 60\\ & \sum F=40& & \sum FD=404\end{array}$

$M.D\left(M\right)=\frac{404}{40}=10.1$

$CoefficientofM.D\left(M\right)=\frac{M.D\left(M\right)}{Median}=\frac{10.1}{54}=0.187$