Calculate the median from the following frequency distribution:
Class | 5 - 10 | 10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 |
Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 2 | 2 |
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.
CLASS | FREQUENCY(fi) | Cf |
5 - 10 | 5 | 5 |
10 - 15 | 6 | 5 + 6 = 11 |
15 - 20 | 15 | 11 + 15 = 26 |
20 - 25 | 10 | 26 + 10 = 36 |
25 - 30 | 5 | 36 + 5 = 41 |
30 - 35 | 4 | 41 + 4 = 45 |
35 - 40 | 2 | 45 + 2 = 47 |
40 - 45 | 2 | 47 + 2 = 49 |
TOTAL | 49 |
So, N = 49
⇒ N/2 = 49/2 = 24.5
The cumulative frequency just greater than (N/2 = ) 24.5 is 25, so the corresponding median class is 15 - 20 and accordingly we get Cf = 11(cumulative frequency before the median class).
Now, since median class is 15 - 20.
∴ l = 15, h = 5, f = 15, N/2 = 24.5 and Cf = 11
Median is given by,
⇒ 
= 15 + 4.5
= 19.5
Thus, median is 19.5.