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Problem: Population Standard Deviation {{10,11,12,13,14},{3,12,18,12,3}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Population Standard Deviation {{10,11,12,13,14},{3,12,18,12,3}}


`x`
`(1)`
Frequency `(f)`
`(2)`
`f*x`
`(3)=(2)xx(1)`
`f*x^2=(f*x)xx(x)`
`(4)=(3)xx(1)`
10330300
11121321452
12182162592
13121562028
14342588
------------
`n=48``sum f*x=576``sum f*x^2=6960`


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

`=576/48`

`=12`



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

`=sqrt((6960 - (576)^2/48)/48)`

`=sqrt((6960 - 6912)/48)`

`=sqrt(48/48)`

`=sqrt(1)`

`=1`








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