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Find 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)/10`
`A=35,h=10`
`(4)`
`f*d`
`(5)=(2)xx(4)`
`f*d^2`
`(6)=(5)xx(4)`
10 - 2015 15 `15=(10+20)/2` -2 `d=(15-35)/10=(-20)/10=-2`
`d=(x-35)/10`
 -30 `-30=15xx-2`
`(5)=(2)xx(4)`
 60 `60=-30xx-2`
`(6)=(5)xx(4)`
20 - 3025 25 `25=(20+30)/2` -1 `d=(25-35)/10=(-10)/10=-1`
`d=(x-35)/10`
 -25 `-25=25xx-1`
`(5)=(2)xx(4)`
 25 `25=-25xx-1`
`(6)=(5)xx(4)`
30 - 4020 35=A `35=(30+40)/2` 0 `d=(35-35)/10=(0)/10=0`
`d=(x-35)/10`
 0 `0=20xx0`
`(5)=(2)xx(4)`
 0 `0=0xx0`
`(6)=(5)xx(4)`
40 - 5012 45 `45=(40+50)/2` 1 `d=(45-35)/10=(10)/10=1`
`d=(x-35)/10`
 12 `12=12xx1`
`(5)=(2)xx(4)`
 12 `12=12xx1`
`(6)=(5)xx(4)`
50 - 608 55 `55=(50+60)/2` 2 `d=(55-35)/10=(20)/10=2`
`d=(x-35)/10`
 16 `16=8xx2`
`(5)=(2)xx(4)`
 32 `32=16xx2`
`(6)=(5)xx(4)`
------------------
`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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