Question

On the sports day of a school, $300$ students participated. Their ages are given in the following distribution.

Age (in years)	$5-7$	$7-9$	$9-11$	$11-13$	$13-15$	$15-17$	$17-19$
Number of students	$67$	$33$	$41$	$95$	$36$	$13$	$15$

Find the mean and mode of the date.

Answer 1

$C.I$	$Frequency$ $f_i$	$Mid-value$ $x_i$	$f_i{x}_i$
$5-7$	$67$	$6$	$402$
$7-9$	$33$	$8$	$264$
$9-11$	$41$	$10$	$410$
$11-13$	$95$	$12$	$1140$
$13-15$	$36$	$14$	$504$
$15-17$	$13$	$16$	$208$
$17-19$	$15$	$18$	$270$
	$\sum f_i=300$		$\sum f_i{x}_i=3198$

$\Rightarrow$ $Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{3198}{300}=10.66$

$\Rightarrow$ Here, Modal class $=11-13$

So, $l=11,f_0=41,f_1=95,f_2=36$ and $h=2$

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

$=11+\frac{95-41}{2\times 85-41-36}\times 2$

$=11+\frac{54}{93}\times 2$

$=11+1.16$

$\therefore$ $Mode=12.16$