Question

Solve problem 2 by step-deviation method.

Answer 1

Take A = 25, h = 4

Age (in years) C.I.	Class marks $\left(x_i\right)$	$$\begin{gathered} d_i=x_i-A \\ {d}_i=x_i-25 \end{gathered}$$	$u_i=\frac{d_i}{h}=\frac{d_i}{4}$	No. of people $\left(f_i\right)$	$f_i{u}_i$
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	$25\to A$	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	-	-	-	$\sum _{}^{}{f}_i=100$	$\sum _{}^{}{f}_i{u}_i=-28$

Now mean u_i s is can be calculated thus:

$$\begin{gathered} \overline{u}=\frac{{\displaystyle \sum _{}^{}}{f}_i{u}_i}{{\displaystyle \sum _{}^{}}{f}_i}=\frac{-28}{100}=-0.28 \\ \mathrm{Mean}=\overline{x}=A+h\overline{u} \\ =25+4\left(-0.28\right) \\ =25-1.12 \\ =23.88 \\ \therefore \mathrm{Mean}\mathrm{age}\mathrm{of}\mathrm{person}s\mathrm{suffering}\mathrm{from}\text{a}\mathrm{sth}\mathrm{ma}\mathrm{is}23.88\mathrm{years}. \end{gathered}$$