SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 1 · Warm-up
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Lepto = peaked, platy = flat, meso = normal; positive skew = long right tail.
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SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 1 · Warm-up – 12 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.
The first central moment of any distribution is always:
Correct Answer: B [zero]
Explanation:
Answer: zero. μ₁ = Σ(x − x̄)/n = 0.
2.
The second central moment of a distribution equals its:
Correct Answer: D [variance]
Explanation:
Answer: variance. μ₂ = Σ(x − x̄)²/n = σ².
3.
For a normal distribution, the value of β₂ is:
Correct Answer: C [3]
Explanation:
The normal curve is mesokurtic: β₂ = 3.
4.
A distribution with β₂ = 4.5 is:
Correct Answer: A [leptokurtic]
Explanation:
β₂ > 3 → more peaked than normal.
5.
In a positively skewed distribution:
Correct Answer: B [mean > median > mode]
Explanation:
The mean is pulled towards the long right tail.
6.
Mean = 52, mode = 46, SD = 12. Karl Pearson's coefficient of skewness is:
Correct Answer: A [0.5]
Explanation:
Answer: 0.5. (52 − 46)/12 = 0.5.
7.
Bowley's coefficient of skewness always lies between:
Correct Answer: D [−1 and +1]
Explanation:
Numerator = difference of two gaps, denominator = their sum.
8.
μ₂ = 5 and μ₃ = −10. What is β₁?
Correct Answer: C [0.8]
Explanation:
Answer: 0.8. β₁ = μ₃²/μ₂³ = 100/125 = 0.8.
9.
Which measure of skewness can be used for a distribution with open-end classes?
Correct Answer: B [Bowley's coefficient]
Explanation:
Bowley's coefficient uses only quartiles and the median.
10.
Statement-basedWhich of the following is/are correct?
I. In a symmetric distribution all odd central moments are zero.
II. If μ₃ = 0, the distribution must be symmetric.
I. In a symmetric distribution all odd central moments are zero.
II. If μ₃ = 0, the distribution must be symmetric.
Correct Answer: A [Only I]
Explanation:
Symmetry ⇒ μ₃ = 0, but μ₃ = 0 does not prove symmetry (e.g.
11.
γ₂ for a platykurtic distribution is:
Correct Answer: D [negative]
Explanation:
Answer: negative. γ₂ = β₂ − 3 < 0 when β₂ < 3.
12.
Match the followingMatch the term with its description:
P. Leptokurtic Q. Platykurtic R. Mesokurtic S. Positive skew
1. Flat-topped, β₂ < 3 2. Long right tail 3. Peaked, β₂ > 3 4. Normal, β₂ = 3
P. Leptokurtic Q. Platykurtic R. Mesokurtic S. Positive skew
1. Flat-topped, β₂ < 3 2. Long right tail 3. Peaked, β₂ > 3 4. Normal, β₂ = 3
Correct Answer: C [P-3, Q-1, R-4, S-2]
Explanation:
Lepto = peaked, platy = flat, meso = normal; positive skew = long right tail.
➤ 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)
Here you get the answer with a one-line explanation. 657 original questions with worked answers · notes, formulas, figures and statistical tables (z, t, χ², F) · practice sets + 3 mock tests
Get the book – ₹149 More quizzes
› SSC CGL Statistics – Mock Test M3 – Mixed Paper II Set (All 12 Chapters)
› SSC CGL Statistics – Mock Test M2 – Probability, Sampling, Inference & ANOVA (Chapters 6–10)
› SSC CGL Statistics – Mock Test M1 – Descriptive Statistics (Chapters 1–5)
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