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 median percentage of marks
Solution:
Given, the table represents the marks and frequency of 100 students in an examination.
We have to determine the median percentage of marks.
| Marks | Frequency | Cumulative frequency |
| 30 - 35 | 14 | 14 |
| 35 - 40 | 16 | 30 |
| 40 - 45 | 18 | 48 |
| 45 - 50 | 23 | 71 |
| 50 - 55 | 18 | 89 |
| 55 - 60 | 8 | 97 |
| 60 - 65 | 3 | 100 |
Median = l + [(n/2 - cf)/f]h
Where, l is lower limit of the median class
n is the number of observations
h is the class size
cf is the cumulative frequency of the class preceding the median class
f is the frequency of the median class
From the table,
n/2 = 100/2 = 50
The observation lies in the class 45 - 50
Lower limit of the class, l = 45
Class size, h = 5
Cumulative frequency of the class preceding the median class, cf = 48
Frequency of the median class, f = 23
Now, median = 45 + [(50 - 48)/23](5)
= 45 + (2/23)5
= 45 + (10/23)
= 45.4
Therefore, the median percentage of marks is 45.4
✦ Try This: 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 |
| Frequency | 12 | 14 | 16 | 22 | 19 | 9 |
Determine the median percentage of marks.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14
NCERT Exemplar Class 10 Maths Exercise 13.3 Sample Problem 3
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 median percentage of marks
Summary:
From the above data, the median percentage of marks obtained by 100 students in an examination is 45.4
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