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Find Standard deviation {85,96,76,108,85,80,100,85,70,95} [ Calculator, Method and examples ]

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Your problem `->` Standard deviation {85,96,76,108,85,80,100,85,70,95}


`x``x - bar x = x - 88``(x - bar x)^2`
85 -3 `-3=85-88` 9 `9=-3xx-3`
96 8 `8=96-88` 64 `64=8xx8`
76 -12 `-12=76-88` 144 `144=-12xx-12`
108 20 `20=108-88` 400 `400=20xx20`
85 -3 `-3=85-88` 9 `9=-3xx-3`
80 -8 `-8=80-88` 64 `64=-8xx-8`
100 12 `12=100-88` 144 `144=12xx12`
85 -3 `-3=85-88` 9 `9=-3xx-3`
70 -18 `-18=70-88` 324 `324=-18xx-18`
95 7 `7=95-88` 49 `49=7xx7`
---------
`sum x=880``sum (x - bar x)=0``sum (x - bar x)^2=1216`


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

`=(85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10`

`=880/10`

`=88`



Population Standard deviation `sigma = sqrt((sum (x - bar x)^2)/n)`

`=sqrt(1216/10)`

`=sqrt(121.6)`

`=11.0272`








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