Find the mode of the following distribution table
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Question:
Find the mode of the following distribution of marks obtained by the students in an examination:
Marks obtained 0-20 20-40 40-60 60-80 80-100
Number of students 15 18 21 29 17
Given the mean of the above distribution is 53, using empirical relationship estimate the value of its median.
ANS:
Here modal class is 60-80, since it has a maximum frequency which is 29.
l= 60 , f1= 29, f0= 21, f2= 17, h= 20
Mode= l + (f1-f0/2f1-f0-f2) ×h
Mode= 60 +(29-21/2×29-21-17)× 20
Mode= 60 + (8/58-21-17)× 20
Mode= 60+ (8/37-17)×20
Mode= 60 + (8/20)×20
Mode = 60 + 8
Mode = 68
Hence, the mode marks is 68.
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