Question
Download Solution PDFIf first, second, and third moment about origin are 1, 6, and 15 respectively, then Karl Pearson beta coefficient of skewness β1 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 1/125
Key PointsGiven:
μ1' = 1; μ2' = 6; μ3' = 15
Calculation:
B1 =
Now, μ2 = μ2' - (μ1')2
⇒ 6 - (1)2
⇒ 5
μ3 = μ3' - 3 (μ2') (μ1') + 2 (μ1')3
⇒ 15 - 3 (6) (1) + 2 (1)3
⇒ 15 - 18 + 2
⇒ -1
By putting the above two values in (1)
⇒ B1 =
⇒ B1 = 1/125
Additional Information
- The Karl Pearson's coefficient of skewness is a measure of the degree of skewness or asymmetry of a probability distribution.
- It is calculated as the third standardized moment about the mean, which is the ratio of the third central moment and the cube of the standard deviation.
- The coefficient of skewness has the following properties:
- If β1 = 0, then the distribution is symmetric and has no skewness.
- If β1 > 0, then the distribution is positively skewed and has a long right tail.
- If β1 < 0, then the distribution is negatively skewed and has a long left tail.
- The coefficient of skewness is an important descriptive statistic that provides information about the shape of a distribution.
- The coefficient of skewness should be used in conjunction with other measures such as the mean, median, and standard deviation to describe the distribution and understand its properties
Last updated on Jul 9, 2025
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