Reach PostNetwork Academy

Moments About an Arbitrary Point (Ungrouped Data)

Definition: The general formula is:

μr' = Σ(xi - A)r / n, where r = 0, 1, 2, 3, 4

• Zero-order moment:
  μ0' = 1
• First-order moment:
  μ1' = Σ(xi - A) / n
• Second-order moment:
  μ2' = Σ(xi - A)2 / n
• Third-order moment:
  μ3' = Σ(xi - A)3 / n
• Fourth-order moment:
  μ4' = Σ(xi - A)4 / n

Moments About an Arbitrary Point (Grouped Data)

Definition: For grouped data:

μr' = Σfi(xi - A)r / N, where N = Σfi, r = 0, 1, 2, 3, 4

• Zero-order moment:
  μ0' = 1
• First-order moment:
  μ1' = Σfi(xi - A) / N
• Second-order moment:
  μ2' = Σfi(xi - A)2 / N

• Third-order

  PDFPresentation

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