Question

The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness β_z ?
1. 0.875
2. 1.125
3. 1.25
4. 4.5

Answer 1

Correct Answer - Option 2 : 1.125

Given

μ₂ = 4

μ₄ = 18

Formula used

Karl pearson's coefficient of skewness β_z = μ₄/μ²₂

Calculaton

Karl Pearson defined the following four coefficients, based upon the first four moments"about mean:

⇒ βz = 18/4²

⇒ βz = 18/16

∴ The value of Pearson's coefficient of skewness βz is 1.125

Moment = The rth moment of a variable x about any point x = A, usually denotted by μ_r' and it is given by

μr' = (1/N)[∑f_i(x_i - A)^r , ∑f_i = N

⇒  (1/N)[∑f_id_i^r  d_i = (x_i - A)

Moment about mean = The rth moments of a variable about the mean x̅  denoted by μ =(1/N)[∑fi(xi - x̅ )r = (1/N)[∑f_iz_i^r  where z_i = xi - x̅