Find the median of the following frequency distribution:
Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
Number of students | 6 | 16 | 30 | 9 | 4 |
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.
MARKS | NUMBER OF STUDENTS(fi) | Cf |
0 - 10 | 6 | 6 |
10 - 20 | 16 | 6 + 16 = 22 |
20 - 30 | 30 | 22 + 30 = 52 |
30 - 40 | 9 | 52 + 9 = 61 |
40 - 50 | 4 | 61 + 4 = 65 |
TOTAL | 65 |
So, N = 65
⇒ N/2 = 65/2 = 32.5
The cumulative frequency just greater than (N/2 = ) 32.5 is 52, so the corresponding median class is 20 - 30 and accordingly we get Cf = 22(cumulative frequency before the median class).
Now, since median class is 20 - 30.
∴ l = 20, h = 10, f = 30, N/2 = 32.5 and Cf = 22
Median is given by,
⇒
= 20 + 3.5
= 23.5
Thus, median is 23.5.