The following data shows the runs scored by different batsmen. Find the modal number of runs scored by the batsmen. Runs ScoredNumber of batsmen3000−400044000−5000185000−600096000−700077000−800068000−900039000−10000110000−110001
A
4608.69
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B
4000
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C
4300
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D
5000
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Solution
The correct option is A 4608.69 Modal calss is the class with the highest frequency. So, the modal class for the given data is 4000-5000. ∵Mode =l+(f1−f02f1−f0−f2)×h
where f1 represents the frequency of the modal class.
Also, l=lower boundary of the modal class h= size of the modal class interval f0= frequency of the class preceding the modal class f2= frequency of the class succeeding the modal class ∴Mode =4000+[(18−42(18)−4−9)]×1000 =4000+[(18−436−4−9)]×1000=4000+[(1423)]×1000=4608.69