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

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


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)`
13 1 `1=1` 3 `3=3xx1`
`(4)=(2)xx(3)`
 3 `3=3xx1`
`(5)=(4)xx(3)`
24 2 `2=2` 8 `8=4xx2`
`(4)=(2)xx(3)`
 16 `16=8xx2`
`(5)=(4)xx(3)`
510 5 `5=5` 50 `50=10xx5`
`(4)=(2)xx(3)`
 250 `250=50xx5`
`(5)=(4)xx(3)`
6 - 1023 8 `8=(6+10)/2` 184 `184=23xx8`
`(4)=(2)xx(3)`
 1472 `1472=184xx8`
`(5)=(4)xx(3)`
10 - 2020 15 `15=(10+20)/2` 300 `300=20xx15`
`(4)=(2)xx(3)`
 4500 `4500=300xx15`
`(5)=(4)xx(3)`
20 - 3020 25 `25=(20+30)/2` 500 `500=20xx25`
`(4)=(2)xx(3)`
 12500 `12500=500xx25`
`(5)=(4)xx(3)`
30 - 5015 40 `40=(30+50)/2` 600 `600=15xx40`
`(4)=(2)xx(3)`
 24000 `24000=600xx40`
`(5)=(4)xx(3)`
50 - 703 60 `60=(50+70)/2` 180 `180=3xx60`
`(4)=(2)xx(3)`
 10800 `10800=180xx60`
`(5)=(4)xx(3)`
70 - 1002 85 `85=(70+100)/2` 170 `170=2xx85`
`(4)=(2)xx(3)`
 14450 `14450=170xx85`
`(5)=(4)xx(3)`
---------------
`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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