Question

The times, in seconds, taken by $150$ athletes to run a $110\mathrm{m}$ hurdle race are tabulated below The number of athletes who completed the race in less than $14.6$ seconds is :

Class	Frequency
$13.8-14$	$2$
$14-14.2$	$4$
$14.2-14.4$	$5$
$14.4-14.6$	$71$
$14.6-14.8$	$48$
$14.8-15$	$20$

• A. $11$
• B. $71$
• C. $82$
• D. $30$

Answer 1

The correct option is C

$82$

Explanation for the correct option.

It is given the time taken by $150$ athletes to run a $110\mathrm{m}$ hurdle race.

Column of cumulative frequency is,

Class	Frequency	Cummulative frequency
$13.8-14$	$2$	$2$
$14-14.2$	$4$	$2+4=6$
$14.2-14.4$	$5$	$6+5=11$
$14.4-14.6$	$71$	$11+71=82$
$14.6-14.8$	$48$	$82+48=130$
$14.8-15$	$20$	$130+20=150$

From the above table, the cumulative frequency written beside the interval $14.4-14.6$ is $82$. We have chosen the interval $14.4-14.6$ because it shows the number of athletes who completed the race before that interval and during that interval, combined.
Therefore, the correct option is (C).