Find the median of the following data.
Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | Total |
Number of students | 8 | 16 | 36 | 34 | 6 | 100 |
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table and convert it into exclusive - type by adjusting from both ends of a class.
MARKS | NUMBER OF STUDENTS(fi) | Cf |
0 - 10 | 8 | 8 |
10 - 20 | 16 | 8 + 16 = 24 |
20 - 30 | 36 | 24 + 36 = 60 |
30 - 40 | 34 | 60 + 34 = 94 |
40 - 50 | 6 | 94 + 6 = 100 |
TOTAL | 100 |
So, N = 100
⇒ N/2 = 100/2 = 50
The cumulative frequency just greater than (N/2 = ) 50 is 60, so the corresponding median class is 20 - 30 and accordingly we get Cf = 24(cumulative frequency before the median class).
Now, since median class is 20 - 30.
∴ l = 20, h = 10, f = 36, N/2 = 50 and Cf = 24
Median is given by,
⇒ 
= 20 + 7.22
= 27.22
Thus, median is 27.22.