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

find the mode of the data.

Answer 1

From the given data we may observe that maximum class frequency is $18$ belonging to class interval $4000–5000.$

So, modal class $=4000–5000$

Lower limit $\left(l\right)$ of modal class $=4000$

Frequency $\left(f_1\right)$ of modal class $=18$

Frequency $\left(f_0\right)$ of class preceding modal class $=4$

Frequency $\left(f_2\right)$ of class succeeding modal class $=9$

Class size $\left(h\right)=1000$

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

$\Rightarrow$ $Mode=4000+\frac{18-4}{2\times 18-4-9}\times 1000$

$\Rightarrow$ $Mode=4000+\frac{14000}{23}$

$\Rightarrow$ $Mode=4000+608.7=4608.7runs$