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 10, 2025
-> The SSC CGL Application Correction Window Link Live till 11th July. Get the corrections done in your SSC CGL Application Form using the Direct Link.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.