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

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


Kurtosis :
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)`
615305-6.45208.0125-1341.6806
64181152-3.45214.245-739.1453
67422814-0.458.505-3.8273
702718902.55175.5675447.6971
7385845.55246.421367.631
------------------
--`n=100``sum f*x=6745``--`=852.75``=-269.325`


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

`=sqrt(852.75/100)`

`=sqrt(8.5275)`

`=2.9202`



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

`=19937.5931/(100*(2.9202)^4)`

`=19937.5931/(100*72.7183)`

`=2.7418`








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