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Question
Following data gives age of 100 students in a school. Calculate variance and S.D.
| Age (In years) | 10 | 11 | 12 | 13 | 14 |
| No. of students | 10 | 20 | 40 | 20 | 10 |
Solution
We prepare the following table for the calculation of variance and S.D:
| Age (In years) xi |
No. of students fi |
fixi | fixi2 |
| 10 | 10 | 100 | 1000 |
| 11 | 20 | 220 | 2420 |
| 12 | 40 | 480 | 5760 |
| 13 | 20 | 260 | 3380 |
| 14 | 10 | 140 | 1960 |
| Total | N = 100 | ∑fixi = 1200 | ∑fixi2 = 14520 |
`bar"x" = (sum"f"_"i""x"_"i")/("N")`
= `(1200)/(100)`
= 12
Var(X) = `σ_"x"^2=(sum"f"_"i""x"_"i"^2)/("N") - (bar"x")^2`
= `(14520)/(100) - (12)^2`
= 145.2 – 144
= 1.2
∴ S.D. = σx = `sqrt("Var"("X"))=sqrt(1.2)`
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