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 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

Find the mode of the data.

Answer 1

From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 − 5000.

Therefore, modal class = 4000 − 5000

Lower limit (l) of modal class = 4000

Frequency (f₁) of modal class = 18

Frequency (f₀) of class preceding modal class = 4

Frequency (f₂) of class succeeding modal class = 9

Class size (h) = 1000

`"Mode" = l + ((f_1-f_0)/(2f_1-f_0-f_2))xxh`

= `4000+((18-4)/(2(18)-4-9))xx1000`

= `4000+(14000/23)`

= 4000 + 608.695

= 4608.695

Therefore, the mode of the given data is 4608.7 runs.