Question

Find the mean deviation about the following continuous distribution:

Marks obtained	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
No. of boys	$6$	$8$	$14$	$16$	$4$	$2$

Answer 1

Givan data

Marks obtained $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

No. of boys $6$ $8$ $14$ $16$ $4$ $2$

Mean deviation about mean

Marks obtained No. of boys($f_i$) Mid value($x_i$) $f_i{x}_i$ $|x_i-\overline{x}|$ $f_i|x_i-\overline{x}|$

$0-10$ $6$ $5$ $30$ $|5-27|=22$ $6\times 22=132$

$10-20$ $8$ $15$ $120$ $|15-27|=12$ $8\times 12=96$

$20-30$ $14$ $25$ $350$ $|25-27|=2$ $14\times 2=28$

$30-40$ $16$ $35$ $560$ $|35-27|=8$ $16\times 8=128$

$40-50$ $4$ $45$ $180$ $|45-27|=18$ $4\times 18=72$

$50-60$ $2$ $55$ $110$ $|55-27|=28$ $2\times 28=56$

Total $50$ $1350$ $512$

Mean$\left(\overline{x}\right)=\sum f_i{x}_i/\sum f_i=\frac{1350}{50}=27$

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

$=\frac{512}{50}$

$=10.24$.