Question

The following table shows the frequency distribution of trees planted by different housing societies in a particular locality.

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

Find the mean number of trees planted by the housing societies by using the step-deviation method.

Answer 1

Take A = 27.5, h = 5

No. of trees C.I.	Class Marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-27.5 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{5}$	No. of societies $\left(f_i\right)$	$f_i{u}_i$
10-15	12.5	$-$15	$-$3	2	$-$6
15-20	17.5	$-$10	$-$2	7	$-$14
20-25	22.5	$-$5	$-$1	9	$-$9
25-30	$27.5\to A$	0	0	8	0
30-35	32.5	5	1	6	6
35-40	37.5	10	2	4	8
Total	-	-	-	$\sum _{}^{}{f}_i=36$	$\sum _{}^{}{f}_i{u}_i=-15$

Now, mean u_i s can be calculated thus:

$$\begin{gathered} \overline{u}=\frac{{\displaystyle \sum _{}^{}}{f}_i{u}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{-15}{36}=-0.417 \\ \mathrm{Mean}=\overline{x}=A+h\overline{u} \\ =27.5+5(-0.417) \\ =27.5-2.085 \\ =25.415\approx 25.42 \\ \therefore \mathrm{The}\mathrm{mean}\mathrm{number}\mathrm{of}\mathrm{trees}\mathrm{planted}\mathrm{by}\text{the}\mathrm{housing}\mathrm{societ}\text{ies}\mathrm{is}25.42. \end{gathered}$$