Answer 1

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. = σ_x = `sqrt("Var"("X"))=sqrt(1.2)`