Question

The following table shows the age distribution of patients of malaria in a village during a particular month.

Age (in years)	$5-14$	$15-24$	$25-34$	$35-44$	$45-54$	$55-64$
No. of cases	$6$	$11$	$21$	$23$	$14$	$5$

Find the average age of the patients.

Answer 1

Converting the series into exclusive form, we get:

Class	Frequency $\left(f_i\right)$	Mid values $\left(x_i\right)$	$u_i=\frac{(xi-A)}{h}$ $=\frac{(x_i-29.5)}{10}$	$\left(f_i{u}_i\right)$
$4.5-14.5$	$6$	$9.5$	$-2$	$-12$
$14.5-24.5$	$11$	$19.5$	$-1$	$-11$
$24.5-34.5$	$21$	$29.5=A$	$0$	$0$
$34.5-44.5$	$23$	$39.5$	$1$	$23$
$44.5-54.5$	$14$	$49.5$	$2$	$28$
$54.5-64.5$	$5$	$59.5$	$3$	$15$
	$\sum f_i=80$			$\sum \left(f_i{u}_i\right)=43$

Now, Assumed Mean, $A=29.5,$ class size $h=10,$

$N=\sum f_i=80$ and $\sum \left(f_i{u}_i\right)=43$

∴ Mean, $\overline{x}=A+h\times \frac{\sum \left(f_i{u}_i\right)}{\sum f_i}$

$=29.5+10\times \frac{43}{80}$

$=29.5+5.375$

$=34.875$

$\therefore \overline{x}=34.875$

Hence, The average age of the patients is $34.87$ years.