Question

Solve problem 6 by assumed-mean method.

Answer 1

No. of trees C.I.	Class Marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-27.5 \end{gathered}$$	No. of societies $\left(f_i\right)$	$f_i{d}_i$
10-15	12.5	$-$15	2	$-$30
15-20	17.5	$-$10	7	$-$70
20-25	22.5	$-$5	9	$-$45
25-30	$27.5\to A$	0	8	0
30-35	32.5	5	6	30
35-40	37.5	10	4	40
Total	-		$\sum _{}^{}{f}_i=36$	$\sum _{}^{}{f}_i{d}_i=-75$

$$\begin{gathered} \overline{d}=\frac{{\displaystyle \sum _{}^{}}{f}_i{d}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{-75}{36}=-2.08 \\ \mathrm{Mean}=\overline{x}=A+\overline{d} \\ =27.5+(-2.08) \\ =27.5-2.08 \\ =25.42 \\ \therefore \mathrm{The}\mathrm{mean}\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{planted}\mathrm{by}\text{the}\mathrm{housing}\mathrm{society}\mathrm{is}25.42. \end{gathered}$$