The following frequency distribution shows the marks obtained by 100 students in a school. Find
the mode.
Marks
Less than 10
Lees than 20
Less than 30
Less than 40
Less than 50
number of students
10
15
30
50
72
Answers
Answered by
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Frequency distribution table:
ci f
i
cf
0−10 7 7
10−20 21−7=14 21
20−30 34−21=13 34
30−40 46−24=12 46
40−50 66−46=20 66
50−60 77−66=11 77
60−70 92−77=15 92
70−80 100−92=8 100
Mode=l+(
2f
1
−f
0
−f
2
f
1
−f
0
)×h
Here,
maximum frequency f
1
=20
⇒ modal class =40−60
lower limit of modal class l=40
class size h=10
preceding frequency of modal class f
0
=12
succeeding frequency of modal class f
2
=11
∴Mode=40+(
40−12−−11
20−12
)×10
∴Mode=40+(
17
8
)×10
∴Mode=44.705≈44.71
And is 44.71
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