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Find Sample skewness {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}}

Solution:
Your problem `->` Sample skewness {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}}


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

`=3650/100`

`=36.5`

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 - 20 15 `15=(10+20)/2`5 75 `75=5xx15`
`(4)=(2)xx(3)`
 -21.5 `|15-36.5|=-21.5`
`|x - 36.5|`
 2311.25 `2311.25=5xx-21.5xx-21.5`
`(6)=(2)xx(5)`
 -49691.875 `-49691.875=2311.25xx-21.5`
`(7)=(2)xx(6)`
 1068375.3125 `1068375.3125=-49691.875xx-21.5`
`(8)=(2)xx(7)`
20 - 30 25 `25=(20+30)/2`18 450 `450=18xx25`
`(4)=(2)xx(3)`
 -11.5 `|25-36.5|=-11.5`
`|x - 36.5|`
 2380.5 `2380.5=18xx-11.5xx-11.5`
`(6)=(2)xx(5)`
 -27375.75 `-27375.75=2380.5xx-11.5`
`(7)=(2)xx(6)`
 314821.125 `314821.125=-27375.75xx-11.5`
`(8)=(2)xx(7)`
30 - 40 35 `35=(30+40)/2`42 1470 `1470=42xx35`
`(4)=(2)xx(3)`
 -1.5 `|35-36.5|=-1.5`
`|x - 36.5|`
 94.5 `94.5=42xx-1.5xx-1.5`
`(6)=(2)xx(5)`
 -141.75 `-141.75=94.5xx-1.5`
`(7)=(2)xx(6)`
 212.625 `212.625=-141.75xx-1.5`
`(8)=(2)xx(7)`
40 - 50 45 `45=(40+50)/2`27 1215 `1215=27xx45`
`(4)=(2)xx(3)`
 8.5 `|45-36.5|=8.5`
`|x - 36.5|`
 1950.75 `1950.75=27xx8.5xx8.5`
`(6)=(2)xx(5)`
 16581.375 `16581.375=1950.75xx8.5`
`(7)=(2)xx(6)`
 140941.6875 `140941.6875=16581.375xx8.5`
`(8)=(2)xx(7)`
50 - 60 55 `55=(50+60)/2`8 440 `440=8xx55`
`(4)=(2)xx(3)`
 18.5 `|55-36.5|=18.5`
`|x - 36.5|`
 2738 `2738=8xx18.5xx18.5`
`(6)=(2)xx(5)`
 50653 `50653=2738xx18.5`
`(7)=(2)xx(6)`
 937080.5 `937080.5=50653xx18.5`
`(8)=(2)xx(7)`
------------------------
----`n=100``sum f*x=3650``--`=9475``=-9975``=2461431.25`


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

`=sqrt(9475/99)`

`=sqrt(95.7071)`

`=9.783`



Skewness `= (sum(x - bar x)^3)/((n-1)*S^3)`

`=-9975/(99*(9.783)^3)`

`=-9975/(99*936.3022)`

`=-0.1076`








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