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Problem: Sample Standard Deviation {{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 ]

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Your problem `->` Sample Standard Deviation {{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)`
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`



Sample Standard deviation `S = sqrt((sum f*x^2 - (sum f*x)^2/n)/(n-1))`

`=sqrt((67991 - (1995)^2/100)/99)`

`=sqrt((67991 - 39800.25)/99)`

`=sqrt(28190.75/99)`

`=sqrt(284.7551)`

`=16.8747`








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