Question

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

Run Scored	Number of Batsman
$3000-4000$	$4$$={\mathrm{f}}_1$
$4000-5000$	$18$$={\mathrm{f}}_{\mathrm{m}}$
$5000-6000$	$9$$={\mathrm{f}}_2$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Answer 1

To find mode, use $\begin{array}{rcl}\mathrm{Mode}& =& \mathrm{l}+\left[\frac{{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_1}{2{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_1-{\mathrm{f}}_2}\right]\times \mathrm{h}\end{array}$

From the given table, we have,

Modal class $=4000–5000$,

$l=4000$, class width $\left(\mathrm{h}\right)=1000$,

${\mathrm{f}}_{\mathrm{m}}=18,{\mathrm{f}}_1=4$and${\mathrm{f}}_2=9$

$\begin{array}{rcl}\mathrm{Mode}& =& \mathrm{l}+\left[\frac{{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_1}{2{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_1-{\mathrm{f}}_2}\right]\times \mathrm{h}\\ & =& 4000+\left[\frac{18-4}{36-4-9}\right]\times 1000\\ & =& 4000+\frac{14000}{23}\\ & =& 4000+608.695\\ & =& 4608.695\\ & =& 4608.7\end{array}$

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