Question

Find the mean deviation about the following continuous distribution:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

Answer 1

Class interval $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

Frequency $5$ $8$ $7$ $12$ $28$ $20$ $10$ $10$

Mean deviation about mean

Class interval frequency($f_i$) Mid value$\left(x_i\right)$ $f_i{x}_i$

$0-10$ $5$ $5$ $25$

$10-20$ $8$ $15$ $120$

$20-30$ $7$ $25$ $175$

$30-40$ $12$ $35$ $420$

$40-50$ $28$ $45$ $1260$

$50-60$ $20$ $55$ $1210$

$60-70$ $10$ $65$ $650$

$70-80$ $10$ $75$ $750$

$\sum f_i=100$

$\sum f_i{x}_i=4610$

Mean $\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{4610}{100}$

$=46.1$

Class interval frequency($f_i$) mid value($x_i$) $|x_i-\overline{x}|$ $f_i|x_i-\overline{x}|$

$0-10$ $5$ $5$ $|5-46.1|=41.1$ $205.5$

$10-20$ $8$ $15$ $|15-46.1|=31.1$ $248.8$

$20-30$ $7$ $25$ $|25-46.1|=21.1$ $147.7$

$30-40$ $12$ $35$ $|35-46.1|=11.1$ $133.2$

$40-50$ $28$ $45$ $|45-46.1|=1.1$ $30.8$

$50-60$ $20$ $55$ $|55-46.1|=8.9$ $178$

$60-70$ $10$ $65$ $|65-46.1|=18.9$ $189$

$70-80$ $10$ $75$ $|75046.1|=28.9$ $289$

Total $100$ _____

$1422$

Mean deviation about mean M.D($\overline{x}$)$=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}$

$=\frac{1422}{100}$

$=14.22$.