Question

Calculate the mean deviation about median for the following data

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

• 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

$\begin{array}{cccccc}{X}_i& 3& 9& 10& 12& 13\\ f_i& 3& 4& 5& 2& 4\\ c.f.& 3& 7& 12& 14& 18\end{array}$

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

Let's calculate $fi|x_i-M|$ for given observations.

$\begin{array}{cccccc}|x_i-M|& 7& 1& 0& 2& 3\\ f_i& 3& 4& 5& 2& 4\\ f_i|x_i-M|& 21& 4& 0& 4& 12\end{array}$

Mean deviation about median=M.D(M)=${\sum }_{i=1}^n\frac{fi|x_i-M|}{{\sum }_{i=1}^{n}fi}$

=$\frac{21+4+0+4+12}{18}$

=$\frac{41}{18}=2.278$ $\therefore M.D\left(M\right)=2.278$.