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Question
The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is ______.
Options
`sqrt(52/7)`
`52/7`
`sqrt(6)`
6
Solution
The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is `sqrt(52/7)`.
Explanation:
Given data are 6, 5, 9, 13, 12, 8 and 10
∴ n = 7
| `x_i` | `x_i^2` |
| 6 | 36 |
| 5 | 25 |
| 9 | 81 |
| 13 | 169 |
| 12 | 144 |
| 8 | 64 |
| 10 | 100 |
| `sumx_i` = 63 | `sumx_i^2` = 619 |
∴ S.D. = `sqrt((sumx_i^2)/n - ((sumx_i)/n)^2`
= `sqrt(619/7 - (63/7)^2`
= `sqrt(619/7 - (9)^2`
= `sqrt(619/7 - 81)`
= `sqrt((619 - 567)/7)`
= `sqrt(52/7)`
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