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

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

Skewness :
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 (x - bar x)^4= (x - 88)^4 85 -3 9 -27 81 96 8 64 512 4096 76 -12 144 -1728 20736 108 20 400 8000 160000 85 -3 9 -27 81 80 -8 64 -512 4096 100 12 144 1728 20736 85 -3 9 -27 81 70 -18 324 -5832 104976 95 7 49 343 2401 --- --- --- --- --- 880 0 1216 2430 317284

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

=sqrt(1216/10)

=sqrt(121.6)

=11.0272

Population Skewness = (sum(x - bar x)^3)/(n*S^3)

=2430/(10*(11.0272)^3)

=2430/(10*1340.9123)

=0.1812

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