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Problem: Population kurtosis {85,96,76,108,85,80,100,85,70,95} [ Calculator, Method and examples ]

Solution:
Your problem -> Population kurtosis {85,96,76,108,85,80,100,85,70,95}

Kurtosis :
Mean bar x = (sum x)/n

=(85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10

=880/10

=88

 x (x - bar x)= (x - 88) (x - bar x)^2= (x - 88)^2 (x - bar x)^3= (x - 88)^3 85 -3 9 -27 96 8 64 512 76 -12 144 -1728 108 20 400 8000 85 -3 9 -27 80 -8 64 -512 100 12 144 1728 85 -3 9 -27 70 -18 324 -5832 95 7 49 343 --- --- --- --- 880 0 1216 2430

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

=sqrt(1216/10)

=sqrt(121.6)

=11.0272

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

=317284/(10*(11.0272)^4)

=317284/(10*14786.56)

=2.1458

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