Question

The following table gives the marks obtained by 50 students in a class test:
Marks
11-15
16-20
21-25
26-30
31-35
36-40
41-45 46-50
2
3
6
7
14
12
4.
2
Number
of students
Calculate the mean, median and mode for the above data.
​

Answer 1

Answer:

ci f

i

cf

10.5−15.5 2 2

15.5−20.5 3 2+3=5

20.5−25.5 6 5+6=11

25.5−30.5 7 11+7=18

30.5−35.5 14 18+14=32

35.5−40.5 12 32+12=44

40.5−45.5 4 44+4=48

45.5−50.5 2 48+2=50

Median =l+

f

m

(

2

N

−cf)

×c

Here,

Class Interval c=5

N=Σf

i

=50

2

N

=25

⇒ Median class =30.5−35.5

⇒Frequency of median classf

m

=14

Lower boundary of median class l=30.5

previous cumulative frequency of median class cf=18

∴ Median =30.5+

14

(

2

50

−18)

×5

∴ Median =30.5+

14

(7)

×5

∴ Median =33