Question

Calculate the mean deviation for the data given here:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$5$	$3$	$9$	$12$	$6$

Answer 1

We have learnt to calculate the mean for grouped data. To calculate the mean deviation, let us first find out the mean and take the deviations from mean. This gives $D$. Computing $\sum |D|$, we can find the mean deviation.

Class interval	Frequency	Mid point $x$	$fx$	Deviaton $D=x-X$	$|D|$	$f|D|$
$0-10$	$5$	$5$	$25$	$5-28.1=-23.1$	$23.1$	$115.5$
$10-20$	$3$	$15$	$45$	$15-28.1=-13.1$	$13.1$	$39.3$
$20-30$	$9$	$25$	$225$	$25-28.1=-3.1$	$3.1$	$27.9$
$30-40$	$12$	$35$	$420$	$35-28.1=6.9$	$6.9$	$82.8$
$40-50$	$6$	$45$	$270$	$45-28.1=16.9$	$16.9$	$101.4$
	$N=35$		$\sum fx=985$			$\sum f|D|=366.9$

$MeanX=\frac{\sum fx}{N}=\frac{985}{35}\approx 28.1$.
Mean deviation $=\frac{\sum f|D|}{N}=\frac{366.9}{35}\approx 10.4$.