Find the median of the following data.

Class interval 0 – 20 20 – 40 40 – 60 60 – 80 80 - 100

Frequency 9 16 24 15 4

Correct option is C

Given:

Class Intervals and Frequencies

0 – 20: 9

20 – 40: 16

40 – 60: 24

60 – 80: 15

80 – 100: 4

Concept Used:

Median = L + $$\left( \frac{\frac{N}{2} - CF}{f} \right) \times h$$​​

Solution:

Where

( L ) = Lower boundary of the median class

( N ) = Total frequency

( CF ) = Cumulative frequency of the class before the median class

( f ) = Frequency of the median class

( h ) = Class width

Total Frequency ( N )

N = 9 + 16 + 24 + 15 + 4 = 68

Median Class

The median is the value at the $$\frac{N}{2}$$​ -th position.

​$$\frac{N}{2} = \frac{68}{2}$$​ = 34

Find the class where the 34th observation lies by calculating cumulative frequencies:

0 – 20: 9

20 – 40: 9 + 16 = 25

40 – 60: 25 + 24 = 49 (This is the median class since 34 lies between 25 and 49)

Identify Median Class Parameters

Median Class: 40 – 60

Lower Boundary ( L ) 40

Before Median Class ( CF ) 25

Median Class ( f ) 24

Class Width ( h ) 20

Median = 40 + $$\left( \frac{34 - 25}{24} \right) \times 20$$​​

Median = 40 + $$\left( \frac{9}{24} \right) \times 20$$​​

Median = 40 + $$\left( \frac{3}{2} \right) \times 5$$​

Median = 40 + 7.5 = 47.5