SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 3 · Challenge
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Mesokurtic → β₂ = 3 → μ₄ = 3μ₂² = 3 × 16² = 768.
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SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 3 · Challenge – 8 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1.
About A = 4, the first four raw moments are 1, 10, 28 and 217. Find μ₃ and μ₄.
Correct Answer: A [μ₃ = 0, μ₄ = 162]
Explanation:
μ₃ = 28 − 3(10)(1) + 2 = 0; μ₄ = 217 − 4(28) + 6(10) − 3 = 162.
2.
For the distribution of the previous question, which description is correct?
Correct Answer: B [β₁ = 0 and platykurtic (β₂ = 2)]
Explanation:
μ₃ = 0 → β₁ = 0; β₂ = 162/81 = 2 < 3 → platykurtic.
3.
Diagram-basedThe histogram shows the scores of 50 players in a fictional quiz league.
What type of skewness does the distribution show?
What type of skewness does the distribution show?
Correct Answer: C [Negative – mean < median < mode]
Explanation:
The long tail is on the left; mean 32.2 < median 32.67 < mode 33.33.
4.
Mean = 40, SD = 10 and Karl Pearson's (median form) coefficient of skewness is 0.6. What is the median?
Correct Answer: D [38]
Explanation:
0.6 = 3(40 − Md)/10 → 40 − Md = 2 → Md = 38.
5.
Which pair (β₁, β₂) is impossible for any data set?
Correct Answer: B [β₁ = 2, β₂ = 2.5]
Explanation:
Answer: β₁ = 2, β₂ = 2.5. β₂ must be ≥ β₁ + 1; 2.5 < 3.
6.
True/False countHow many of the following statements are true?
(i) β₁ can never be negative.
(ii) Central moments are unaffected by a change of origin.
(iii) For y = 3x, μ₄(y) = 3μ₄(x).
(iv) For a symmetric distribution Bowley's coefficient is zero.
(i) β₁ can never be negative.
(ii) Central moments are unaffected by a change of origin.
(iii) For y = 3x, μ₄(y) = 3μ₄(x).
(iv) For a symmetric distribution Bowley's coefficient is zero.
Correct Answer: A [Three]
Explanation:
(i), (ii), (iv) true; μ₄(3x) = 3⁴μ₄(x) = 81μ₄(x).
7.
Q₃ − Md = 18 and Md − Q₁ = 12 for a distribution. Bowley's coefficient of skewness is:
Correct Answer: A [0.2]
Explanation:
(18 − 12)/(18 + 12) = 6/30 = 0.2.
8.
A mesokurtic distribution has standard deviation 4. What is its fourth central moment μ₄?
Correct Answer: D [768]
Explanation:
Mesokurtic → β₂ = 3 → μ₄ = 3μ₂² = 3 × 16² = 768.
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics
📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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