Question

Question 5
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

$\begin{array}{cc}\text{Runs scored}& Numberofbatsmen\\ 3000-4000& 4\\ 4000-5000& 18\\ 5000-6000& 9\\ 6000-7000& 7\\ 7000-8000& 6\\ 8000-9000& 3\\ 9000-10000& 1\\ 10000-11000& 1\end{array}$

Find the mode of the data.

Answer 1

From the given data, we observe that maximum class frequency is 18 belonging to class interval 4000 - 5000.

So, modal class = 4000 - 5000

Lower limit $l$ 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 $h$ = 1000

$\text{Now,mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h=4000+\left(\frac{18-4}{2\left(18\right)-4-9}\right)\times 1000=4000+\left(\frac{14000}{23}\right)$

= 4608.695

So, mode of given data is 4608.7 runs.