Question

Find the moment coefficient of Skewness and kurtosis for the dat below. a) 9, 3, 4, 2, 9, 5,

Answer 1

Given.

9,3,4,2,9,5

(a) Skewness

$\mu_3=\dfrac{\sum (x_i-\mu)^3}{(n-1)\sigma^3}$

$\mu = \dfrac{\sum X_i}{N}$

$\mu=\dfrac{9+3+4+2+9+5}{6} =5.33$

$\sigma=\sqrt\dfrac{(X_i -u)^2}{N}$

$\sigma=\sqrt \dfrac{45.34}{6}= 2.75$

$\mu_3=\dfrac{46.57}{5(2.75)^3}=0.448$

(b) Kurtosis

$Kurt (X)=\dfrac{\mu^4}{\sigma^4}$

$\mu^4=\dfrac{\sum(X_i -\mu)^4}{N}$

$\mu^4=\dfrac{518.39}{6}=86.40$

$Kurt (X) =\dfrac{86.40}{57.19}=1.51$