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 4000−5000 5000−6000 6000−7000	4 18 9 7	7000−8000 8000−9000 9000−10000 10000−11000	6 3 1 1

Find the mode of data.

Answer 1

The given data is shown below.

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

Here, the maximum frequency is 18 so the modal class is 4000-5000.

Therefore,

$$\begin{gathered} \therefore \mathrm{Mode}=l+\frac{f-f_1}{2f-f_1-f_2}\times h \\ =4000+\frac{18-4}{2\times 18-4-9}\times 1000 \\ =4000+\frac{14}{23}\times 1000 \\ =4000+608.7 \\ =4608.7 \end{gathered}$$

Thus, the mode of the data (or runs scored) is 4608.7.