Compute the median from the following data:
Marks | 0 - 7 | 7 - 14 | 14 - 21 | 21 - 28 | 28 - 35 | 35 - 42 | 42 - 49 |
Number of students | 3 | 4 | 7 | 11 | 0 | 16 | 9 |
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 - 7 | 3 | 3 |
7 - 14 | 4 | 3 + 4 = 7 |
14 - 21 | 7 | 7 + 7 = 14 |
21 - 28 | 11 | 14 + 11 = 25 |
28 - 35 | 0 | 25 + 0 = 25 |
35 - 42 | 16 | 25 + 16 = 41 |
42 - 49 | 9 | 41 + 9 = 50 |
TOTAL | 50 |
So, N = 50
⇒ N/2 = 50/2 = 25
The cumulative frequency just greater than (N/2 = ) 25 is 41, so the corresponding median class is 35 - 42 and accordingly we get Cf = 25(cumulative frequency before the median class).
Now, since median class is 35 - 42.
∴ l = 35, h = 7, f = 16, N/2 = 25 and Cf = 25
Median is given by,
⇒ 
= 35 + 0
= 35
Thus, median marks are 35.