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Problem: Population Variance {{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 Variance {{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)/10`
`A=35,h=10`
`(4)`
`f*d`
`(5)=(2)xx(4)`
`f*d^2`
`(6)=(5)xx(4)`
10 - 201515-2-3060
20 - 302525-1-2525
30 - 402035=A000
40 - 50124511212
50 - 6085521632
------------------
`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 Variance `sigma^2 = ((sum f*d^2 - (sum f*d)^2/n)/n) * h^2`

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

`=((129 - 9.1125)/80) * 100`

`=119.8875/80 * 100`

`=1.4986 * 100`

`=149.8594`








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