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Question
Answer the following :
Compute the variance and S.D. for the following data:
| X | 62 | 30 | 64 | 47 | 63 | 46 | 35 | 28 | 60 |
| F | 5 | 8 | 3 | 4 | 5 | 7 | 8 | 3 | 7 |
Solution
| xi | fi | fixi | xi2 | fixi2 |
| 62 | 5 | 310 | 3844 | 19220 |
| 30 | 8 | 240 | 900 | 7200 |
| 64 | 3 | 192 | 4096 | 12288 |
| 47 | 4 | 188 | 2209 | 8836 |
| 63 | 5 | 315 | 3969 | 19845 |
| 46 | 7 | 322 | 2116 | 14812 |
| 35 | 8 | 280 | 1225 | 9800 |
| 28 | 3 | 84 | 784 | 2352 |
| 60 | 7 | 420 | 3600 | 25200 |
| N = 50 | `sumf_"i"x_"i"` = 2351 | `sumf_"i"x_"i"^2` = 119553 |
`bar(x) = (sumf_"i"x_"i")/"N" = 2351/50` = 47.02
Var (X) = `sigma_x^2 = (sumf_"i"x_"i"^2)/"N" - (barx)^2`
= `119553/50 - (47.02)^2`
= 2391.06 – 2210.88
= 180.18
S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(180.18)`
= 13.42
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