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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)`
103 30 `30=3xx10`
`(3)=(2)xx(1)`
 300 `300=30xx10`
`(4)=(3)xx(1)`
1112 132 `132=12xx11`
`(3)=(2)xx(1)`
 1452 `1452=132xx11`
`(4)=(3)xx(1)`
1218 216 `216=18xx12`
`(3)=(2)xx(1)`
 2592 `2592=216xx12`
`(4)=(3)xx(1)`
1312 156 `156=12xx13`
`(3)=(2)xx(1)`
 2028 `2028=156xx13`
`(4)=(3)xx(1)`
143 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`


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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