7. Solve problem 2 by 'Step Deviation Method'.
Following table gives age distribution of people suffering from 'Asthma due to air pollution in certain city.
| Age in years | 7-11 | 11-15 | 15-19 | 19-23 | 23-27 | 27-31 | 31-35 | 35-39 |
| No. of people | 5 | 9 | 13 | 21 | 16 | 15 | 12 | 9 |
Sol. Class width ($h$) = 4, Assumed mean ($A$) = 25
Age in years Class Mark ($x_i$) $d_i = x_i - A$ $u_i = \frac{d_i}{h}$ No. of people ($f_i$) $f_i u_i$ 7 - 11 9 - 16 - 4 5 - 20 11 - 15 13 - 12 - 3 9 - 27 15 - 19 17 - 8 - 2 13 - 26 19 - 23 21 - 4 - 1 21 - 21 23 - 27 25 → A 0 0 16 0 27 - 31 29 4 1 15 15 31 - 35 33 8 2 12 24 35 - 39 37 12 3 9 27 Total 100 - 28 $$ \bar{u} = \frac{\sum f_i u_i}{\sum f_i} $$
$$ \therefore \bar{u} = \frac{-28}{100} $$
$$ \therefore \bar{u} = -0.28 $$$$ \text{Mean } (\bar{x}) = A + h\bar{u} $$
$$ = 25 + 4(-0.28) $$
$$ = 25 - 1.12 $$
$$ = 23.88 \text{ years} $$