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प्रश्न
A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
उत्तर
The remaining number of pages to be completed is 60 – 32, 60 – 35, 60 – 37, 60 – 30, 60 – 33, 60 – 36, 60 – 35 and 60 – 37
The pages to be completed are, 28, 25, 23, 30, 27, 24, 25, and 23
Arrange in ascending order we get, 23, 23, 24, 25, 25, 27, 28 and 30
| xi | xi2 |
| 23 | 529 |
| 23 | 529 |
| 24 | 576 |
| 25 | 625 |
| 25 | 625 |
| 27 | 729 |
| 28 | 784 |
| 30 | 900 |
| `sumx_"i"` = 205 | `sumx_"i"^2` = 5297 |
Here n = 8, `sumx_"i"` = 205, `sumx_"i"^2` = 5297
Standard deviation (σ) = `sqrt((sumx_"i"^2)/"n" - ((sumx_"i")/"n")^2`
= `sqrt(5297/8 - (205/8)^2`
= `sqrt(662.13 - 42025/64)`
= `sqrt(662.13 - 656.64)`
= `sqrt(5.49)`
= 2.34
Standard deviation (σ) = 2.34
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