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

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


Kurtosis :
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)`
10 - 201515225-16.6254145.8594-68924.9121
20 - 302525625-6.6251097.2656-7269.3848
30 - 4035207003.375227.8125768.8672
40 - 50451254013.3752146.687528711.9453
50 - 6055844023.3754371.125102175.0469
---------------------
----`n=80``sum f*x=2530``--`=11988.75``=55461.5625`


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

`=sqrt(11988.75/79)`

`=sqrt(151.7563)`

`=12.3189`



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

`=3968995.2539/(79*(12.3189)^4)`

`=3968995.2539/(79*23029.9834)`

`=2.1815`








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