# 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

#### Solution

We prepare the following table for the calculation of variance and S.D:

 Age (In years)xi No. of studentsfi 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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