6. Following table gives 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 number of trees planted by housing society by using 'step deviation method'.
Sol.
Class width ($h$) = 5, Assumed mean ($A$) = 22.5
No. of trees Class Mark ($x_i$) $d_i = x_i - A$ $u_i = \frac{d_i}{h}$ No. of societies ($f_i$) $f_i u_i$ 10 - 15 12.5 $-10$ $-2$ 2 $-4$ 15 - 20 17.5 $-5$ $-1$ 7 $-7$ 20 - 25 22.5 $\rightarrow A$ 0 0 9 0 25 - 30 27.5 5 1 8 8 30 - 35 32.5 10 2 6 12 35 - 40 37.5 15 3 4 12 Total 36 21 $$ \begin{align*} \bar{u} &= \frac{\sum f_i u_i}{\sum f_i} \\ \therefore \bar{u} &= \frac{21}{36} \\ \therefore \bar{u} &= 0.583 \\ \text{Mean } (\bar{x}) &= A + h\bar{u} \\ &= 22.5 + 5(0.583) \\ &= 22.5 + 2.92 \\ &= 25.42 \end{align*} $$