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Problem: Population Variance {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Population Variance {{1,2,5,6-10,10-20,20-30,30-50,50-70,70-100},{3,4,10,23,20,20,15,3,2}}


Class
`(1)`
Frequency `(f)`
`(2)`
Mid value `(x)`
`(3)`
`f*x`
`(4)=(2)xx(3)`
`f*x^2=(f*x)xx(x)`
`(5)=(4)xx(3)`
13133
242816
510550250
6 - 102381841472
10 - 2020153004500
20 - 30202550012500
30 - 50154060024000
50 - 7036018010800
70 - 10028517014450
---------------
`n = 100`-----`sum f*x=1995``sum f*x^2=67991`


Mean `bar x = (sum fx)/n`

`=1995/100`

`=19.95`



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

`=(67991 - (1995)^2/100)/100`

`=(67991 - 39800.25)/100`

`=28190.75/100`

`=281.9075`








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