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Problem: Population Standard Deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} [ Calculator, Method and examples ]

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Your problem -> Population Standard Deviation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}}

 Class(1) Frequency (f)(2) Mid value (x)(3) d=(x-A)/h=(x-35)/10A=35,h=10(4) f*d(5)=(2)xx(4) f*d^2(6)=(5)xx(4) 10 - 20 15 15 -2 -30 60 20 - 30 25 25 -1 -25 25 30 - 40 20 35=A 0 0 0 40 - 50 12 45 1 12 12 50 - 60 8 55 2 16 32 --- --- --- --- --- --- n = 80 ----- ----- sum f*d=-27 sum f*d^2=129

Mean bar x = A + (sum fd)/n * h

=35 + -27/80 * 10

=35 + -0.3375 * 10

=35 + -3.375

=31.625

Population Standard deviation sigma = sqrt((sum f*d^2 - (sum f*d)^2/n)/n) * h

=sqrt((129 - (-27)^2/80)/80) * 10

=sqrt((129 - 9.1125)/80) * 10

=sqrt(119.8875/80) * 10

=sqrt(1.4986) * 10

=1.2242 * 10

=12.2417

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