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

Solution:
Your problem -> Population 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 - 20 15 5 75 -21.5 2311.25 -49691.875 20 - 30 25 18 450 -11.5 2380.5 -27375.75 30 - 40 35 42 1470 -1.5 94.5 -141.75 40 - 50 45 27 1215 8.5 1950.75 16581.375 50 - 60 55 8 440 18.5 2738 50653 --- --- --- --- --- --- --- -- -- n=100 sum f*x=3650 -- =9475 =-9975

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

=sqrt(9475/100)

=sqrt(94.75)

=9.734

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

=2461431.25/(100*(9.734)^4)

=2461431.25/(100*8977.5625)

=2.7418`

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