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Find Population Variance {{10,3},{11,12},{12,18},{13,12},{14,3}}

Solution:
Your problem -> Population Variance {{10,3},{11,12},{12,18},{13,12},{14,3}}

 x(1) Frequency (f)(2) f*x(3)=(2)xx(1) f*x^2=(f*x)xx(x)(4)=(3)xx(1) 10 3 30 30=3xx10(3)=(2)xx(1) 300 300=30xx10(4)=(3)xx(1) 11 12 132 132=12xx11(3)=(2)xx(1) 1452 1452=132xx11(4)=(3)xx(1) 12 18 216 216=18xx12(3)=(2)xx(1) 2592 2592=216xx12(4)=(3)xx(1) 13 12 156 156=12xx13(3)=(2)xx(1) 2028 2028=156xx13(4)=(3)xx(1) 14 3 42 42=3xx14(3)=(2)xx(1) 588 588=42xx14(4)=(3)xx(1) --- --- --- --- n=48 sum f*x=576 sum f*x^2=6960

Mean bar x = (sum fx)/n

=576/48

=12

Population Variance sigma^2 = (sum f*x^2 - (sum f*x)^2/n)/n

=(6960 - (576)^2/48)/48

=(6960 - 6912)/48

=48/48

=1

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