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प्रश्न
In a study about viral fever, the number of people affected in a town were noted as Find its standard deviation
| Age in years | 0−10 | 10−20 | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 |
| Number of people affected | 3 | 5 | 16 | 18 | 12 | 7 | 4 |
उत्तर
Assumed mean = 35
| Age in year |
Number of people affected fi |
Mid value xi |
di = xi − A = xi − 35 |
fidi | fidi2 |
| 0−10 | 3 | 5 | − 30 | − 90 | 2700 |
| 10−20 | 5 | 15 | − 20 | − 100 | 2000 |
| 20−30 | 16 | 25 | − 10 | − 160 | 1600 |
| 30−40 | 18 | 35 | 0 | 0 | 0 |
| 40−50 | 12 | 45 | 10 | 120 | 1200 |
| 50−60 | 7 | 55 | 20 | 140 | 2800 |
| 60−70 | 4 | 65 | 30 | 120 | 3600 |
| `sumf_"i"` = 65 | `sumf_"i""d"_"i"` = 30 | `sumf_"i""d"_"i"^2` = 13900 |
Here `sumf_"i"` = 65, `sumf_"i""d"_"i"` = 30, `sumf_"i""d"_"i"^2` = 13900
Standard deviation (σ) = `sqrt((sumf_"i""d"_"i"^2)/(sumf_"i") - ((sumf_"i"d_"i")/(sumf_"i"))^2`
= `sqrt(13900/65 - (30/65)^2`
= `sqrt(213.85 - (0.46)^2`
= `sqrt(213.85 - 0.21)`
= `sqrt(213.64)`
= 14.616
= 14.62
∴ Standard deviation (σ) = 14.62
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