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Problem: Population skewness {{61,5},{64,18},{67,42},{70,27},{73,8}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Population skewness {{61,5},{64,18},{67,42},{70,27},{73,8}}


Skewness :
Mean `bar x=(sum f x)/n`

`=6745/100`

`=67.45`

`x`
`(2)`
`f`
`(3)`
`f*x`
`(4)=(2)xx(3)`
`(x-bar x)`
`(5)`
`f*(x-bar x)^2`
`(6)=(3)xx(5)`
`f*(x-bar x)^3`
`(7)=(5)xx(6)`
`f*(x-bar x)^4`
`(8)=(5)xx(7)`
615305-6.45208.0125-1341.68068653.84
64181152-3.45214.245-739.14532550.0511
67422814-0.458.505-3.82731.7223
702718902.55175.5675447.69711141.6277
7385845.55246.421367.6317590.352
---------------------
--`n=100``sum f*x=6745``--`=852.75``=-269.325``=19937.5931`


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

`=sqrt(852.75/100)`

`=sqrt(8.5275)`

`=2.9202`



Population Skewness `= (sum(x - bar x)^3)/(n*S^3)`

`=-269.325/(100*(2.9202)^3)`

`=-269.325/(100*24.9019)`

`=-0.1082`








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