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 data given above, 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 (\(f_1\)) of modal class = 18
Frequency (\(f_0\)) of class preceding the modal class = 4
Frequency (\(f_2\)) of class succeeding the modal class = 9
Class size (\(h\)) = 1000

Mode = \(l\) + \((\frac{f_1 - f_0 }{2f_1 - f_0 - f_2)} \times h\)

Mode = \(4000 + (\frac{18 - 4 }{ 2(18) - 4 - 9}) \times1000\)

Mode =\(4000+ [\frac{14000}{23}]\)

Mode = 4000 + 608.695
Mode = 4608.695

Therefore, mode of the given data is 4608.7 runs.