Question

Find the median of the following frequency distribution:

Marks 0-10 10-20 20-30 30-40 40-50 Total

No. of Students 8 20 36 24 12 100​

Answer 1

Answer:

point

(m) frequency

(f) (m-25)/10

(d) fd c.f.

0-10 5 12 -2 -24 12

10-20 15 13 -1 -13 25

20-30 25 25 0 0 50

30-40 35 20 1 20 70

40-50 45 10 2 20 80

n=80 ∑fd=3

Median is given by L+

f

2

n

−c.f.

×i

where L is the lower limit of the median class. (median class is the class where

2

n

th

term is lying)

c.f. is the cumulative frequency of the class preceding the median class

f is the frequency of the median class

i is the class interval of the median class.

From the above table,

L=20

2

n

=40

c.f.=25

f=25

i=10

Therefore, median=20+

25

40−25

×10=20+6=26