Page 4 - Lesson Note MCT 2 54

26
= 20 + = 20 + 6.5 = 26.5
4

Ex: - Find the missing frequency in the following distribution if N=100 and
median=30.

Marks (X) 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60
Number of students (F) 10 ? 25 30 ? 10

Answer: - calculation of missing frequency.

Let the missing frequencies of class interval 10 – 20 and 40 – 50 be x and
y respectively.

Marks (X) Frequency (F) Cumulative Frequency (C.F)

0 – 10 10 10
10 – 20 X 10+x
20 – 30 25 35+x
30 – 40 30 65+x

40 – 50 Y 65+x+y
50 - 60 10 75+x+y=100
= ∑ = 75 + + = 100

=> + = 100 − 75 = 25 ----------------------- (1)

In the question it is given as, median = 30, Median class = 30 – 40.

= 30, f =30, c. f = 35+x, i = 10.
1
100
Median = ℎ ℎ = = 50th data
2 2
− .
Median = + 2 × => 30 = 30 + 50−(35+ ) 10
1
30
50−35− 15−
=> 30 − 30 = => 0 = => 0 = 15 −
3 3
=> = 15, Substituting the value of x=15 in equation (1) we get y=10.