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Question
Answer the following :
Find variance and S.D. for the following set of numbers:
25, 21, 23, 29, 27, 22, 28, 23, 21, 25
Solution
We construct the following table to compute variance and S.D.:
| xi | ui = xi – A A = 25 |
ui2 |
| 25 | 0 | 0 |
| 21 | – 4 | 16 |
| 23 | – 2 | 4 |
| 29 | 4 | 16 |
| 27 | 2 | 4 |
| 22 | – 3 | 9 |
| 28 | 3 | 9 |
| 23 | – 2 | 4 |
| 21 | – 4 | 16 |
| 25 | 0 | 0 |
| `sumu_"i"` = – 6 | `sumu_"i"^2` = 78 |
From the table,
`sumu_"i"` = – 6, `sumu_"i"^2` = 78, n = 10
∴ Var(x) = `sigma_x^2 = sigma_u^2 = (sumu_"i"^2)/"n" - ((sumu_"i")/"n")^2`
= `78/10 - ((-6)/10)^2`
= 7.8 – 0.36
= 7.44
S.D. = `sqrt("Var(x)")`
= `sqrt(7.44)`
= 2.72
Hence, variance = 7.44 and S.D. = 2.72
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