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प्रश्न
The following table shows the age distribution of patients of malaria in a village during a particular month:
| Age (in years) | 5 – 14 | 15 – 24 | 25 – 34 | 35 – 44 | 45 – 54 | 55 - 64 |
| No. of cases | 6 | 11 | 21 | 23 | 14 | 5 |
Find the average age of the patients.
उत्तर
| Class | Frequency `(f_i)` |
Mid values `(x_i)` |
`u_i = ((x_i− A))/ ℎ = ((x_i− 29.5))/ 10` |
`(f_i × u_i)` |
| 4.5 – 14.5 | 6 | 9.5 | -2 | -12 |
| 14.5 – 24.5 | 11 | 19.5 | -1 | -11 |
| 24.5 – 34.5 | 21 | 29.5 = A | 0 | 0 |
| 34.5 – 44.5 | 23 | 39.5 | 1 | 23 |
| 44.5 – 54.5 | 14 | 49.5 | 2 | 28 |
| 54.5 – 64.5 | 5 | 59.5 | 3 | 15 |
| `Ʃ f_i` = 80 | `Ʃ (f_i × u_i)` = 43 |
Now, `A = 29.5, h = 10, Ʃ f_i = 80 and Ʃ (f_i × u_i) = 43`
∴ Mean, 𝑥 =`A + { ( Ʃ (f_i × u_i))/(Ʃ f_i)}`
= `29.5 + {10 xx 43/80}`
=29.5 + 5.375
= 34.875
∴ 𝑥 = 34.875
∴ The average age of the patients is 34.87 years.
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