Question

The following distribution gives ages of $1000$ persons who visited a shopping centre on sunday:

Age(in years)	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Number of persons	$105$	$222$	$220$	$138$	$102$	$113$	$100$

Use step deviation method, find the mean number of the people who visited the shopping centre on Sunday.

Answer 1

$\Rightarrow$ $A=35$ and $h=10$

$C.I$	$Classmark$ $x_i$	$d_i=x_i-A$	$u_i=\frac{d_i}{h}$	$f_i$	$f_i{u}_i$
$0-10$	$5$	$-30$	$-3$	$105$	$-315$
$10-20$	$15$	$-20$	$-2$	$222$	$-444$
$20-30$	$25$	$-10$	$-1$	$220$	$-220$
$30-40$	$35$	$0$	$0$	$138$	$0$
$40-50$	$45$	$10$	$1$	$102$	$102$
$50-60$	$55$	$20$	$2$	$113$	$226$
$60-70$	$65$	$30$	$3$	$100$	$300$
				$\sum f_i=1000$	$\sum f_i{u}_i=-351$

$\Rightarrow$ Required mean $=A+\frac{\sum f_i{u}_i}{\sum f_i}\times h$

$=35+\frac{(-351)}{1000}\times 10$

$=35-3.51$

$=31.49$