Question

Calculate mean deviation from the median of the following data :

$\begin{array}{cccccc}\text{Class Interval :}& 0-6& 6-12& 12-18& 18-24& 24-30\\ \text{Frequency :}& 4& 5& 3& 6& 2\end{array}$

Answer 1

$\begin{array}{cccccc}\text{Class Interval}& \text{Mid values}& f_i& c.f.& |x_i-14|& f_i|x_i-14|\\ 0-6& 3& 4& 4& 11& 44\\ 6-12& 9& 5& 9& 5& 25\\ 12-18& 15& 3& 12& 1& 3\\ 18-24& 21& 6& 18& 7& 42\\ 24-30& 27& 2& 20& 13& 26\\ & & N=25& & & \sum f_i|x_i-14|=40\end{array}$

Here, N = 20, so $=\frac{N}{2}=10$

The cumulative frequency just greater than $\frac{N}{2}$ is 12.

Thus, 12-18 is the median class

Now, l = 12, h = 6., f = 3 and F = 9

$\therefore$ Median $=l+\frac{\frac{N}{2}-F}{f}\times h=12+\left(\frac{10-9}{3}\right)\times 6=14$

Now,

Mean deviation about the median $=\frac{1}{N}\sum f_i|x_i-14|=\frac{1}{20}\times 140=7$