Question

Calculate the mean deviation from median and coefficient of MD from the given data

$\begin{array}{cc}\text{X}& \text{Frequency}\\ 12& 8\\ 18& 12\\ 25& 15\\ 35& 23\\ 47& 16\\ 55& 18\\ 62& 31\\ 75& 12\end{array}$

Answer 1

Calculation of Mean Deviation from Median Coefficient of Mean Deviation

$\begin{array}{ccccc}\text{x}& \text{Frequency}& \text{Cumulative Frequency}& |D|=|X-M|& f|D|\\ & \left(f\right)& \left(cf\right)& M=47& \\ 12& 8& 8& 35& 280\\ 18& 12& 20& 29& 348\\ 25& 15& 35& 22& 330\\ 35& 23& 58& 12& 276\\ 47& 16& 74& 0& 0\\ 55& 18& 92& 8& 144\\ 62& 31& 123& 15& 465\\ 75& 12& 135& 28& 336\\ & N=135& & & \sum f|D|=2179\end{array}$

Median = Size of $\left(\frac{N+1}{2}\right)$th item

= Size of $\left(\frac{135+1}{2}\right)$th item

= Size of $\left(\frac{136}{2}\right)$th item

68th item lies in 74 cumulative frequency hence, median (M) = 47

Mean Deviation (MD) = $\frac{MD}{Median}=\frac{16.14}{47}=0.34$