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

Solution:
Your problem -> Sample 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 - 20 15 15 225 -16.625 4145.8594 -68924.9121 20 - 30 25 25 625 -6.625 1097.2656 -7269.3848 30 - 40 35 20 700 3.375 227.8125 768.8672 40 - 50 45 12 540 13.375 2146.6875 28711.9453 50 - 60 55 8 440 23.375 4371.125 102175.0469 --- --- --- --- --- --- --- -- -- 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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