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प्रश्न
The following table shows the age of patients admitted in a hospital during a particular week:
| Age (in years): | 5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 |
| Number of patients: | 5 | 12 | 20 | 24 | 15 | 4 |
Find the mean age of patients.
योग
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उत्तर
Given
| Class | `(x_i)` | `(f_i)` | `(u_i = \frac{x_i - 30}{10})` | `(f_i u_i)` |
|---|---|---|---|---|
| 5-15 | 10 | 5 | -2 | -10 |
| 15-25 | 20 | 12 | -1 | -12 |
| 25-35 | 30 | 20 | 0 | 0 |
| 35-45 | 40 | 24 | 1 | 24 |
| 45-55 | 50 | 15 | 2 | 30 |
| 55-65 | 60 | 4 | 3 | 12 |
| `N = 80` | `\sum f_i u_i = 44` |
Formula
\[ \overline{X} = A + h\left(\frac{\sum f_i u_i}{N}\right) \]
Substitution
\[ \overline{X} = 30 + 10 \times \frac{44}{80} \]
\[ \overline{X} = 30 + 5.5 \]
Final answer
\[ \overline{X} = 35.5 \text{ years} \]
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