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Question

The marks in the science of 80 students of class X are given below: Find the mode of the marks obtained by the students in science.
Marks:0-1010-2020-3030-4040-5050-6060-7070-8080-9090-100
Frequency:35161213205411

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Solution


Marks Frequency
0-10 3
10-20 5
20-30 16
30-40 12
40-50 13
50-60 20
60-70 5
70-80 4
80-90 1
90-100 1
N = 80
As frequency is maximum for the class 5060, modal class is 5060.
Mode=l+f1f02f1(f0+f2)×h
where,
l= lower limit of modal class =50
f1= frequency of modal class =20
f0= frequency of class preceeding the modal class =13
f2= frequency of class succeeding the modal class =5
h= higher limit - lower limit =6050=10

Mode=50+20132×20(13+5)×10

mode=50+722×10
=50+3.18
=53.18


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