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Problem: Population skewness {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} [ Calculator, Method and examples ]

Solution:
Your problem `->` Population skewness {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}}


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

`=2530/80`

`=31.625`

Class
`(1)`
Mid value (`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)`
10 - 201515225-16.6254145.8594-68924.91211145876.6638
20 - 302525625-6.6251097.2656-7269.384848159.6741
30 - 4035207003.375227.8125768.86722594.9268
40 - 50451254013.3752146.687528711.9453384022.2686
50 - 6055844023.3754371.125102175.04692388341.7207
------------------------
----`n=80``sum f*x=2530``--`=11988.75``=55461.5625``=3968995.2539`


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

`=sqrt(11988.75/80)`

`=sqrt(149.8594)`

`=12.2417`



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

`=55461.5625/(80*(12.2417)^3)`

`=55461.5625/(80*1834.5345)`

`=0.3779`








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