Question

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​

Answer 1

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