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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 | 4 | 7000-8000 | 6 |
4000-5000 | 18 | 8000-9000 | 3 |
5000-6000 | 9 | 9000-10000 | 1 |
6000-7000 | 7 | 10000-11000 | 1 |
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$(f_i$): |
3000-4000 | 4 |
4000-5000 | 18 |
5000-6000 | 9 |
6000-7000 | 7 |
7000-8000 | 6 |
8000-9000 | 3 |
9000-10000 | 1 |
10000-11000 | 1 |
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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