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Question
The rainfall recorded in various places of five districts in a week are given below. Find its standard deviation
| Rainfall (in mm) | 45 | 50 | 55 | 60 | 65 | 70 |
| Number of places | 5 | 13 | 4 | 9 | 5 | 4 |
Solution
Assumed mean = 60
| Rainfall (in mm) |
Number of places fi |
di = xi − A = xi − 60 |
fidi | fidi2 |
| 45 | 5 | − 15 | − 75 | 1125 |
| 50 | 13 | − 10 | − 130 | 1300 |
| 55 | 4 | − 5 | − 20 | 100 |
| 60 | 9 | 0 | 0 | 0 |
| 65 | 5 | 5 | 25 | 125 |
| 70 | 4 | 10 | 40 | 400 |
| `sumf_"i"` = 40 | `sumf_"i""d"_"i"` = − 160 | `sumf_"i""d"_"i"^2` = 3050 |
Here N = 40 (N = fi), `sumf_"i""d"_"i"` = − 160, `sumf_"i""d"_"i"^2` = 3050
Standard deviation (σ) = `sqrt((sumf_"i""d"_"i"^2)/"N" - ((sumf_"i""d"_"i")/"N")^2`
= `sqrt(3050/40 - ((- 160)/40)^2`
= `sqrt(76.25 - ( - 4)^2`
= `sqrt(76.25 - 16)`
= `sqrt(60.25)`
= 7.76
∴ Standard deviation (σ) = 7.76
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