Question

The following table shows the ages of the patients admitted in a hospital during a year.Find the mode of the given data.

Age (in years)	$5-15$	$15-25$	$25-35$	$35-45$	$45-55$	$55-65$
No. of patients	$6$	$11$	$21$	$23$	$14$	$5$

Answer 1

Age	Number of patients $\left(f_i\right)$	Class mark$\left(x_i\right)$	$f_i\times x_i$
$5-15$	$6$	$\frac{5+15}{2}=10$	$6\times 10=60$
$15-25$	$11$	$\frac{15+25}{2}=20$	$11\times 20=220$
$25-35$	$21\to \left(f_0\right)$	$\frac{25+35}{2}=30$	$21\times 30=630$
$35-45$	$23\to \left(f_1\right)$	$\frac{35+45}{2}=40$	$23\times 40=920$
$45-55$	$14\to \left(f_2\right)$	$\frac{45+55}{2}=50$	$14\times 50=700$
$55-65$	$5$	$\frac{55+65}{2}=60$	$5\times 60=300$
	$\sum f_i=80$		$\sum f_i{x}_i=2830$

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

Modal class$=$Interval with highest frequency$=35-45$

where $l=$lower limit of modal class$=35$

$h=$Class interval$=15-5=10$

$f_1=$frequency of the modal class $=23$

$f_0=$frequency of the class before modal class$=21$

$f_2=$frequency of the class after modal class$=14$

Mode$=35+\frac{23-21}{2\left(23\right)-21-14}\times 10$

$=35+\frac{2}{46-35}\times 10$

$=35+\frac{2}{11}\times 10=35+1.8=36.8$