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Problem: Sample kurtosis {{10-20,20-30,30-40,40-50,50-60},{5,18,42,27,8}} [ Calculator, Method and examples ]

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


Kurtosis :
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)`
10 - 2015575-21.52311.25-49691.875
20 - 302518450-11.52380.5-27375.75
30 - 4035421470-1.594.5-141.75
40 - 50452712158.51950.7516581.375
50 - 6055844018.5273850653
---------------------
----`n=100``sum f*x=3650``--`=9475``=-9975`


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

`=sqrt(9475/99)`

`=sqrt(95.7071)`

`=9.783`



Sample Kurtosis `= (sum(x - bar x)^4)/((n-1)*S^4)`

`=2461431.25/(99*(9.783)^4)`

`=2461431.25/(99*9159.8434)`

`=2.7143`








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