a) Find the moment coefficient of Skewness and kurtosis for the data below.
9, 3, 4, 2, 9, 5, 8, 4, 7, 4
Skewness:
μ3=∑(xi−μ)3(n−1)σ3\mu_3=\frac{\sum (x_i-\mu)^3}{(n-1)\sigma^3}μ3=(n−1)σ3∑(xi−μ)3
μ=∑xi/n=5.5\mu=\sum x_i/n=5.5μ=∑xi/n=5.5
σ=(xi−μ)2n=2.42\sigma=\sqrt{\frac{(x_i-\mu)^2}{n}}=2.42σ=n(xi−μ)2=2.42
μ3=0.302\mu_3=0.302μ3=0.302
kurtosis:
kurt(X)=μ4σ4kurt(X)=\frac{\mu^4}{\sigma^4}kurt(X)=σ4μ4
μ4=∑(xi−μ)4n\mu^4=\frac{\sum(x_i-\mu)^4}{n}μ4=n∑(xi−μ)4
kurt(X)=1.443kurt(X)=1.443kurt(X)=1.443
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