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Question
The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day :
| Age (in years) | No. of Patients |
| 10-20 | 60 |
| 20-30 | 42 |
| 30-40 | 55 |
| 40-50 | 70 |
| 50-60 | 53 |
| 60-70 | 20 |
Find the median age of the patients.
Solution
| Age (in years) | No. of Patients | c.f. (less than type) |
| 10-20 | 60 | 60 |
| 20-30 | 42 | 102 → c.f. |
|
30-40 Median class |
55 → f | 157 |
| 40-50 | 70 | 227 |
| 50-60 | 53 | 280 |
| 60-70 | 20 | 300 |
Here, N =` 300/2`
N=150
Cumulative frequency just greater than 150 is 157.
∴ Corresponding class (30 – 40) is the median class.
L = 30, f = 55, c.f. = 102, h = 10
`"Median =L"+("N"/2-"c.f")"h"/"f"`
=`30 + (150 - 102) xx(10/55)`
=`30+48 xx (10/55)`
= `30 + 480/55`
=30 + 8.7272
=38.73
Thus, the median age of patients is 38.73 years.
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