Question

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
$\begin{array}{cccc}\text{Runs scored}& \text{Number of bastsman}& \text{Runs scored}& \text{Number of bastsman}\\ 3000-4000& 4& 7000-8000& 6\\ 4000-5000& 18& 8000-9000& 3\\ 5000-6000& 9& 9000-10000& 1\\ 6000-7000& 7& 10000-11000& 1\end{array}$
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 (l) of modal class = 4000

Frequency (f) of modal class = 18

Frequency (f₁) of class preceding modal class = 4

Frequency (f₂) of class succeeding modal class = 9

Class size (h) = 1000

Now

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

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

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

$=4000+608.695=4608.695$

So mode of given data is 4608.7 runs