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Question
The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.
| Age (years) | Less than 5 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 | 25 - 29 |
| No. of patients | 38 | 32 | 50 | 36 | 24 | 20 |
Solution
| Class Age (years) |
Continuous class | Frequency (No. of patients) |
| Less than 5 | 0 − 4.5 | 38 |
| 5 − 9 | 4.5 − 9.5 | 32 → f0 |
| 10 − 14 | 9.5 − 14.5 | 50 → f1 |
| 15 − 19 | 14.5 − 19.5 | 36 → f2 |
| 20 − 24 | 19.5 − 24.5 | 24 |
| 25 − 29 | 24.5 − 29.5 | 20 |
Here, the maximum frequency is 50.
The class corresponding to this frequency is 9.5 - 14.5.
So, the modal class is 9.5 - 14.5.
L = Lower class limit of the modal class = 9.5
h = Class interval of the modal class = 5
f1 = frequency of the modal class = 50
f0 = frequency of the class preceding the modal class = 32
f2 = frequency of the class succeeding the modal class = 36
∴ Mode = `"L" + ((f_1 − f_0)/(2 f_1 − f_0 − f_2)) × h`
= `9.5 + ((50 - 32)/(2(50) - 32 - 36)) × 5`
= `9.5 + ((18)/(100 - 68)) × 5`
= 9.5 + 0.5625 × 5
= 9.5 + 2.8125
∴ The mode of the ages of the patients is 12.31 years (approx.).
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