Find the median from the following data:
Marks | No. of students |
Below 10 | 12 |
Below 20 | 32 |
Below 30 | 57 |
Below 40 | 80 |
Below 50 | 92 |
Below 60 | 116 |
Below 70 | 164 |
Below 80 | 200 |
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.
MARKS | Cf | NUMBER OF STUDENTS(fi) |
0 - 10 | 12 | 12 |
10 - 20 | 32 | 32 - 12 = 20 |
20 - 30 | 57 | 57 - 32 = 25 |
30 - 40 | 80 | 80 - 57 = 23 |
40 - 50 | 92 | 92 - 80 = 12 |
50 - 60 | 116 | 116 - 92 = 24 |
60 - 70 | 164 | 164 - 116 = 48 |
70 - 80 | 200 | 200 - 164 = 36 |
TOTAL | 200 |
So, N = 200
⇒ N/2 = 200/2 = 100
The cumulative frequency just greater than (N/2 = )100 is 116, so the corresponding median class is 50 - 60 and accordingly we get Cf = 92(cumulative frequency before the median class).
Now, since median class is 50 - 60.
∴ l = 50, h = 10, f = 24, N/2 = 100 and Cf = 92
Median is given by,
⇒ 
= 50 + 3.33
= 53.33
Thus, median is 53.33.