Question

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

Marks obtained	10- 20	20- 30	30- 40	40- 50	50- 60	60- 70	70- 80
Number of students	2	3	8	14	8	3	2

• A. $12$
• B. $10$
• C. $11$
• D. $9$

Answer 1

Answer: (B)

We make the following table from the given data.

Marks obtained	Number of students$f_i$	Mid points $x_i$	$f_i{x}_i$	$|x_i-\bar{x}|$	$f_i|x_i-\bar{x}|$
10-20	2	15	30	30	60
20-30	3	25	75	20	60
30-40	8	35	280	10	80
40-50	14	45	630	0	0
50-60	8	55	440	10	80
60-70	3	65	195	20	60
70-80	2	75	150	30	60
	40		1800		400

Here, $N=\sum _{i=1}^7{f}_i=40$,
$\sum _{i=1}^7{f}_i{x}_i=1800$,
$\sum _{i=1}^7{f}_i\left|x_i-\bar{x}\right|=400$
Therefore $\bar{x}=\frac{1}{N}\sum _{i=1}^7{f}_i{x}_i=\frac{1800}{40}=45$
and M.D. $\left(\bar{x}\right)=\frac{1}{N}\sum _{i=1}^7{f}_i\left|x_i-\bar{x}\right|=\frac{1}{40}\times 400=10$