Question

Calcualte the mean deviation of the following income groups of five and seven members from their medians:-

I income in Rs.	II Income in Rs.
4000	3800
4200	4000
4400	4200
4600	4400
4800	4600

Answer 1

Calculate the deviation of the following income groups of five & five members from their medians.

$I$ Income in Rs.	$II$ Income in Rs.
4000	3800
4200	4000
4400	4200
4600	4400
4800	4600

Here no of members in $n=5$ i.e. odd so median is $\frac{n+1}{2}th$ form

$=\frac{5+1}{2}th$ term

$=3th$ term

Median $=4400$

Group $I$

Mean deviation their mediar $=\frac{\sum |x-M|}{5}$

$=\frac{1200}{5}$

$=240$

Group $II$

income in Rs. $x$ $38004000420044004600$

Here no. of memners is $n=5$ i.e odd

so median is middle term median is $4200$

$\begin{array}{cccccc}x& 3800& 400& 4200& 4400& 4600\\ |x-M|& |3800-4200|& |4000-4200|& |4200-4200|& |4400-4200|& |4600-4200|\\ & 400& 200& 0& 200& 400\end{array}$

$\sum |x-M|=1200$

Group $II$

Mean deviation their mediam $=\frac{\sum |x-M|}{5}$

$=\frac{1200}{5}$

$=240$