SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 2 · Exam Level · Paper II Sprint

← Back

SSC CGL Statistics – Moments, Skewness & Kurtosis – Level 2 · Exam Level · Paper II Sprint – 15 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.

Get daily current affairs & exam alerts – follow us YouTube WhatsApp Channel Telegram Channel Facebook Page Instagram
Share with friends & study groups
Link to this page from your website / blog (HTML code)
1.  
About A = 10, the first two raw moments of a distribution are 2 and 20. What is the variance?

Correct Answer: C [16]

Explanation:

μ₂ = μ′₂ − μ′₁² = 20 − 4 = 16.

2.  
About A = 10, the first three raw moments are 2, 20 and 40. What is μ₃?

Correct Answer: B [−64]

Explanation:

μ₃ = 40 − 3(20)(2) + 2(8) = 40 − 120 + 16 = −64.

3.  
The mean of a distribution is 30 and the first three raw moments about A = 30 are therefore:

Correct Answer: A [0, μ₂ and μ₃]

Explanation:

When A = mean, μ′₁ = 0 and raw moments equal central moments.

4.  
μ₂ = 9 and μ₄ = 230. Which statement about the distribution is correct?

Correct Answer: D [It is platykurtic]

Explanation:

3μ₂² = 243 > 230 → β₂ = 230/81 ≈ 2.84 < 3 → platykurtic.

5.  
Mean = 60, median = 63, SD = 15. Karl Pearson's (median form) coefficient of skewness is:

Correct Answer: C [−0.6]

Explanation:

Answer: −0.6. 3(60 − 63)/15 = −9/15 = −0.6.

6.  
Q₁ = 24, median = 30, Q₃ = 33. Bowley's coefficient of skewness is:

Correct Answer: A [−0.33]

Explanation:

(33 + 24 − 60)/(33 − 24) = −3/9 = −1/3.

7.  
The mean is 45, Karl Pearson's coefficient of skewness is −0.4 and the SD is 5. What is the mode?

Correct Answer: D [47]

Explanation:

Mode = Mean − Sk × σ = 45 + 2 = 47.

8.  
For a variable x, μ₃ = 12. If y = 5 − 2x, what is μ₃ of y?

Correct Answer: B [-96]

Explanation:

Answer: -96. μ₃(y) = (−2)³ × 12 = −96.

9.  
Two-quantity comparisonGiven that x has β₂ = 2.6 and y = 4x + 7:
Quantity I: β₂ of x
Quantity II: β₂ of y

Correct Answer: C [Quantity I = Quantity II]

Explanation:

β₂ is a pure number, unchanged by change of origin and scale.

10.  
Assertion–Reason
A: In a negatively skewed distribution the mean is less than the mode.
R: The mean is pulled towards the longer tail of the distribution.

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

Negative skew has its long tail on the left; the mean moves left, below the mode.

11.  
Odd one outwhich of these is NOT a measure of skewness?

Correct Answer: D [β₂]

Explanation:

Answer: β₂. β₂ measures kurtosis.

12.  
Fill in the blankSheppard's correction for grouping is NOT applied to the ______ moment.

Correct Answer: B [third central]

Explanation:

μ₃ needs no correction; μ₂ and μ₄ are corrected.

13.  
A grouped distribution with class width 12 has μ₂ = 40. What is its μ₂ after Sheppard's correction?

Correct Answer: C [28]

Explanation:

Answer: 28. 40 − 12²/12 = 40 − 12 = 28.

14.  
P₁₀ = 15, P₅₀ = 35, P₉₀ = 65. Kelly's coefficient of skewness is:

Correct Answer: C [0.2]

Explanation:

(65 + 15 − 70)/(65 − 15) = 10/50 = 0.2.

15.  
Spot My Mistake“μ₂ = 4, μ₃ = 8, so β₁ = μ₃/μ₂ = 2.” What is the correct β₁?

Correct Answer: D [1]

Explanation:

Answer: 1. β₁ = μ₃²/μ₂³ = 64/64 = 1.

➤ 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 ₹299 →
Score: 0 Answered: 0 / 0