Question
Download Solution PDFThe second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness βz ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
μ2 = 4
μ4 = 18
Formula used
Karl pearson's coefficient of skewness βz = 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
Important Points
Moment = The rth moment of a variable x about any point x = A, usually denotted by μr' and it is given by
μr' = (1/N)[∑fi(xi - A)r , ∑fi = N
⇒ (1/N)[∑fidir di = (xi - 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)[∑fizir where zi = xi - x̅
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