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Question
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 |
| No. of patients | 5 | 20 | 40 | 50 | 25 |
Solution
We prepare the cumulative frequency table, as shown below:
| Age (in years) | Number of patients `(f_i)` | Cumulative Frequency (cf) |
| 0 – 15 | 5 | 5 |
| 15 – 30 | 20 | 25 |
| 30 – 45 | 40 | 65 |
| 45 – 60 | 50 | 115 |
| 60 – 75 | 25 | 140 |
| Total | `N = Σ f_i` = 140 |
Now, N = 140 ⇒`N/2 = 70`
The cumulative frequency just greater than 70 is 115 and the corresponding class is 45 –60
Thus, the median class is 45 – 60.
∴ l = 45, h = 15, f = 50, N = 140 and cf = 65.
Now,
Median = l + `((N/2-cf)/f) xx h`
=`45 + ((140/2-65)/50) xx 15`
=`45+((70-65)/50) xx 15`
= 45 + 1.5
= 46.5
Hence, the median age is 46.5 years.
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