Question

The percentage of marks obtained by 100 students in
an examination are given below:
Marks 30-35 35-40 40-45 45-50 50-55 55-60 60-65
Frequency 14 16 18 23 18 8 3
Determine the mode and median of marks.

Answer 1

Step-by-step explanation:

The formula for getting the median is given by:

Median = L + {(N/2 - C)h} / f

Where :

L = lower limit of the median class.

N = Total frequency

C = Cumulative frequency of the class preceding the median class.

h = The class interval

f = frequency of the median class.

The cumulative frequency of the group data is :

10,26,44,67,85,93,100

The median class:

100/2 = 50

This lies in class 45 - 50

Doing the substitution:

L = 44.5

N = 100

C = 44

h = (50.5 - 44.5 ) = 6

f = 23

We have :

median = 44.5 + {(100/2 - 44)6}/23

Median = 44.5 + 1.565

= 46.065