Question

Calculate the mean deviation about median for the following data

$\begin{array}{cccccc}X& 3& 9& 10& 12& 13\\ F& 3& 4& 5& 2& 4\end{array}$

• A. 2.21
• B. 2.27
• C. 2.56
• D. 2.43

Answer 1

The correct option is B

2.27

The observations are already in ascending order.

Let's calculate the cumulative frequencies

$\begin{array}{cccccc}X& 3& 9& 10& 12& 13\\ F& 3& 4& 5& 2& 4\\ CF& 3& 7& 12& 14& 18\end{array}$

Median of the observations would be the average of $9^{th}$ and ${10}^{th}$ readings
$=\frac{9thterm+10thterm}{2}=\frac{10+10}{2}=10$

Let's calculate $F|X-M|$ for given observations.

$\begin{array}{cccccc}D=|X-M|& 7& 1& 0& 2& 3\\ F& 3& 4& 5& 2& 4\\ FD& 21& 4& 0& 4& 12\end{array}$

$M.D\left(M\right)=\frac{\sum FD}{\sum F}=\frac{21+4+0+4+12}{18}=\frac{41}{18}=2.278$

$\therefore M.D\left(M\right)=2.278$.