Question

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Find the mode of the data.

Answer 1

Mode: The class which have highest frequency.

In this case, class interval $4000-5000$ is the modal class.

Now,

Lower limit of modal class, $l=4000,h=1000,f_1,=18,f_0=4,f_2=9$

We know that,

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

$=4000+\left(\frac{18-4}{2\left(18\right)-4-9}\right)\times 1000$

$=4000+\left(\frac{14}{36-13}\right)1000$

$=4000+\left(\frac{14}{23}\right)\times 1000$

Mode $=4680.7$

Hence, the mode of the given data is $4608.7$ runs.