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Question
Find the Standard Deviation of the following data: 14, 22, 9, 15, 20, 17, 12, 11.
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Solution
Calculate the Mean:
`barX = (14 + 22 + 9 + 15 + 20 + 17 + 12 + 11)/8`
= `120/8`
= 15
Deviations from actual mean.
| Sl. No. | Values(X) | `X - barX` | `(X - barX)^2` |
| 1 | 14 | 14 − 15 = −1 | 1 |
| 2 | 22 | 22 − 15 = 7 | 49 |
| 3 | 9 | 9 − 15 = −6 | 36 |
| 4 | 15 | 15 − 15 = 0 | 0 |
| 5 | 20 | 20 − 15 = 5 | 25 |
| 6 | 17 | 17 − 15 = 2 | 4 |
| 7 | 12 | 12 − 15 = −3 | 9 |
| 8 | 11 | 11 − 15 = −4 | 16 |
| N = 8 | 120 | 0 | 140 |
σ = `sqrt(((sum(x - barx)^2)/"n"))`
= `sqrt(140/8)`
= `sqrt(17.5)`
= 4.18
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