Question

Compute first 4 moments about arithmetic mean from the data .

6,5,4,7,13,5,4,3,8,5

Answer 1

$\mu=(6+5+4+7+13+5+4+3+8+5)/10=6$

First moment equal 0

Second moment

$\frac{\sum_i(x_i-\mu)^2}{10}=\frac{0+1+4+1+49+1+4+9+4+1}{10}=7.4$

Third moment

$\frac{\sum_i(x_i-\mu)^3}{10}=\frac{0+1+8+1+343+1+8+27+8+1}{10}=39.8$

Foth moment

$\frac{\sum_i(x_i-\mu)^4}{n}=\frac{0+1+16+1+2401+1+16+81+16+1}{10}=253.3$