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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 - Mathematics and Statistics

Sum

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
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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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