In a class test, 50 students obtained marks as follows:
Marks obtained | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 |
Number of students | 4 | 6 | 25 | 10 | 5 |
Find the modal class and the median class.
Here, the maximum class frequency is 25.
The class corresponding to this frequency is the modal class. ⇒ modal class = 40 - 60
To find median class,
Assume Σfi = N = Sum of frequencies,
fi = frequency
and Cf = cumulative frequency
Lets form a table.
MARKS OBTAINED | NUMBER OF STUDENTS(fi) | Cf |
0 - 20 | 4 | 4 |
20 - 40 | 6 | 4 + 6 = 10 |
40 - 60 | 25 | 10 + 25 = 35 |
60 - 80 | 10 | 35 + 10 = 45 |
80 - 100 | 5 | 45 + 5 = 50 |
TOTAL | 50 |
So, N = 50
⇒ N/2 = 50/2 = 25
The cumulative frequency just greater than (N/2 = ) 25 is 35, so the corresponding median class is 40 - 60.
∴ modal class = 40 - 60 and median class = 40 - 60