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प्रश्न
Following data gives age of 100 students in a college. Calculate variance and S.D.
| Age (In years) | 16 | 17 | 18 | 19 | 20 | 21 |
| No. of Students | 20 | 7 | 11 | 17 | 30 | 15 |
उत्तर
Let u = `(x - "A")/"h" = (x - 19)/1`
Calculation of variance of u:
| Age (in years) (xi) | No. of Students (fi) | ui = `(x_"i" - 19)/1` | fiui | fiui2 |
| 16 | 20 | – 3 | – 60 | 180 |
| 17 | 7 | – 2 | – 14 | 28 |
| 18 | 11 | – 1 | – 11 | 11 |
| 19 | 17 | 0 | 0 | 0 |
| 20 | 30 | 1 | 30 | 30 |
| 21 | 15 | 2 | 30 | 60 |
| N = 100 | `sumf_"i"u_"i"` = – 25 | `sumf_"i"u_"i"^2` = 309 |
`bar(u) = (sumf_"i"u_"i")/"N" = (-25)/100` = – 0.25
Var (u) = `sigma_u^2 = (sumf_"i"u_"i"^2)/"N" - (baru)^2 = 309/100 - (-0.25)^2`
= 3.09 – 0.0625
= 3.0275
∴ Var (X) = h2 Var (u) = (1)2 (3.0275) = 3.0275
∴ S.D. = `sigma_x = sqrt("Var(X)")`
= `sqrt(3.0275)`
= 1.74
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