The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Runs scoredNumber of batsmanRuns scored
Number of batsman
3000-400047000-80006
4000-5000188000-90003
5000-600099000-100001
6000-7000710000-110001

Find the mode of the data."



Given:

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

To do:

We have to find the mode of the data.

Solution:

The frequency of the given data is as given below.

Runs scored($x_i$):Number of batsman$(f_i$):
3000-40004
4000-500018
5000-60009
6000-70007
7000-80006
8000-90003
9000-100001
10000-110001

We observe that the class interval of 4000-5000 has the maximum frequency(18).

Therefore, it is the modal class.

Here,

$l=4000, h=1000, f=18, f_1=4, f_2=9$

We know that,

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

$=4000+\frac{18-4}{2 \times 18-4-9} \times 1000$

$=4000+\frac{14}{36-13} \times1000$

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

$=4000+608.7$

$=4608.7$

The mode of the given data is 4608.7.

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