Question

The following table shows the ages of the patients admitted in a hospital during a year:

Age(in years )	5-15	15-25	25-35	35-45	45-55	55-65
Number of patients	6	11	21	23	14	5

Find the mode and the mean of the data given above. Compare and interpret the two measure of central tendency.

Answer 1

$Age$	$No.ofpatients$ $f_i$	$Class-mark$ $x_i$	$f_i{x}_i$
$5-15$	$6$	$10$	$60$
$15-25$	$11$	$20$	$220$
$25-35$	$21$	$30$	$630$
$35-45$	$23$	$40$	$920$
$45-55$	$14$	$50$	$700$
$55-65$	$5$	$60$	$300$
	$\sum f_i=80$		$\sum f_i{x}_i=2830$

$\Rightarrow$ $Mean\left(\overline{x}\right)=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{2830}{80}=35.37$

$\Rightarrow$ Modal class $=35-45$

$l=35,h=10,f_0=21,f_1=23,f_2=14$

$\Rightarrow$ $Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

$=35+\frac{23-21}{2\times 23-21-14}\times 10$

$=35+1.81$

$=36.81$

The mode of the data shows that maximum number of patients is in the age group of $36.81$, while average age of all the patients is $\mathrm{35.37.}$