In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.
Age (in years) | 0 - 15 | 15 - 30 | 30 - 45 | 45 - 60 | 60 - 75 |
Number of patients | 5 | 20 | 40 | 50 | 25 |
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.
AGE(years) | NUMBER OF PATIENTS(fi) | Cf |
0 - 15 | 5 | 5 |
15 - 30 | 20 | 5 + 20 = 25 |
30 - 45 | 40 | 25 + 40 = 65 |
45 - 60 | 50 | 65 + 50 = 115 |
60 - 75 | 25 | 115 + 25 = 140 |
TOTAL | 140 |
So, N = 140
⇒ N/2 = 140/2 = 70
The cumulative frequency just greater than (N/2 = ) 70 is 115, so the corresponding median class is 45 - 60 and accordingly we get Cf = 65(cumulative frequency before the median class).
Now, since median class is 45 - 60.
∴ l = 45, h = 15, f = 50, N/2 = 70 and Cf = 65
Median is given by,
⇒
= 45 + 1.5
= 46.5
Thus, median age is 46.5 years.