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Solution
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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 ]
Solution:
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)` | | 1 | 3 | 1 | 3 | 3 | | 2 | 4 | 2 | 8 | 16 | | 5 | 10 | 5 | 50 | 250 | | 6 - 10 | 23 | 8 | 184 | 1472 | | 10 - 20 | 20 | 15 | 300 | 4500 | | 20 - 30 | 20 | 25 | 500 | 12500 | | 30 - 50 | 15 | 40 | 600 | 24000 | | 50 - 70 | 3 | 60 | 180 | 10800 | | 70 - 100 | 2 | 85 | 170 | 14450 | | --- | --- | --- | --- | --- | | `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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Solution provided by AtoZmath.com
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