Question

Find the mean deviation about the mean for the following data.

Answer 1

Given that

Marks obtained $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$

No. of students $2$ $3$ $8$ $14$ $8$ $3$ $2$

Mean deviation about mean

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

$10-20$ $2$ $15$ $30$ $|15-45|=30$ $2\times 30=60$

$20-30$ $3$ $25$ $75$ $|25-45|=20$ $3\times 20=60$

$30-40$ $8$ $35$ $280$ $|35-45|=10$ $8\times 10=80$

$40-50$ $14$ $45$ $630$ $|45-45|=0$ $14\times 0=0$

$50-60$ $8$ $55$ $440$ $|55-45|=10$ $8\times 10=80$

$60-70$ $3$ $65$ $195$ $|65-45|=20$ $3\times 20=60$

$70-80$ $2$ $75$ $150$ $|35-45|=30$ $2\times 30=60$

Total $40$ $1800$ $400$

Mean $\left(\overline{x}\right)=\sum f_i{x}_i/\sum f_i=\frac{1800}{40}$

$=45$

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

$=\frac{400}{40}$

$=10$.