Question

The mean deviation of the following data from mean is :

Class interval	0-5	5-10	10-15	15-20	20-25
Frequency	3	4	8	10	5

• A. $5$
• B. $4$
• C. $6$
• D. $3$

Answer 1

The correct option is A $5$

Class	$x_i$	$f_i$	$u_i=\frac{x_i-A}{h}$	$f_i{u}_i$	$|x_i-\overline{x}|$	$f_i|x_i-\overline{x}|$
0-5	2.5	3	-2	-6	10.33	30.99
5-10	7.5	4	-1	-4	5.33	21.32
10-15	12.5	8	0	0	0.33	2.56
15-20	17.5	10	1	10	4.67	46.7
20-25	22.5	5	2	10	9.67	48.35
Total		30		10		149.92

Where $A$ is the assumed mean i.e. $A=12.5$
Mean $\overline{x}=A+\frac{\sum f_i{u}_i}{\sum f_i}$
$=12.5+\frac{10}{30}=12.83$
Mean deviation about mean $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}$
$=\frac{149.92}{30}=4.998\approx 5$