Question
Download Solution PDFIf the population kurtosis of the observations 16,12,6,2,4,10 is 1.7414, then population kurtosis of the 8,6,3,1,2,5 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is 1.7414
Key Points
- Kurtosis = Fourth Moment / (Second Moment)2
| Variable (x) | Deviation(x - x̄) | Deviation2 | Deviation4 | |
| 8 | 3.8333 | 14.6944 | 215.9267 | |
| 6 | 1.8333 | 3.3611 | 11.2971 | |
| 3 | -1.1667 | 1.3611 | 1.8526 | |
| 1 | -3.1667 | 10.0278 | 100.5563 | |
| 2 | -2.1667 | 4.6944 | 22.0378 | |
| 5 | 0.8333 | 0.6944 | 0.4823 | |
| SUM | 25 | 0 | 34.8333 | 352.1528 |
| SUM/n | x̄ = 4.1667 | 0 | 5.8056 | 58.6921 |
Kurtosis = 58.6921/(5.8056)2
Kurtosis = 1.7414
Important Points
- An attribute of a dataset can be described using the statistical measure kurtosis. On a graph, regularly distributed data typically resembles an upside-down bell when plotted. The bell curve is a name for this. The tails on either side of the curve are often formed by the plotted data that are most dispersed from the data mean. Kurtosis reveals how much information is included in the tails.
- Leptokurtic (below normal), platykurtic (above normal), and mesokurtic (normal) are the three categories of kurtosis (more than normal).
- Only when combined with standard deviation is kurtosis beneficial. Even if an investment has a high kurtosis (poor), the overall standard deviation is likely to be modest (good). On the other hand, a low kurtosis (excellent) investment could have a large total standard deviation (bad).
Hence, if the population kurtosis of the observations 16,12,6,2,4,10 is 1.7414, then the population kurtosis of the 8,6,3,1,2,5 is 1.7414
Last updated on Jul 14, 2025
-> 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.