Question

Following table gives frequency distribution of trees planted by different housing societies in a particular locality.
Find mean number of trees planted by housing society by using 'step deviation method'.

No. of tress	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35	35 - 40
No. of Societies	2	7	9	8	6	4

• A. $25.42$ trees
• B. $27.42$ trees
• C. $29.42$ trees
• D. $31.42$ trees

Answer 1

Answer: (A)

$25.42$ trees

Consider the following table, to calculate mean by "step deviation method":

$x_i$=mid value of class interval

Assumed mean $a=27.5$

class interval $c=5$

$ci$	$f_i$	$x_i$	$u_i=\frac{x_i-a}{c}$	$f_i{u}_i$
10-15	2	12.5	$\frac{12.5-27.5}{5}=$-3	-6
15-20	7	17.5	-2	-14
20-25	9	22.5	-1	-9
25-30	8	27.5	0	0
30-35	6	32.5	1	6
35-40	4	37.5	2	8

$N=\Sigma f_i=36$

$\Sigma f_i{u}_i=-15$

Mean $\overline{x}=a+\frac{\Sigma f_i{u}_i}{N}\times c$

$\therefore \overline{x}=27.5+\frac{-15}{36}\times 5=25.42$

Hence, option $A$ is corect.