SSC CGL Statistics – Mock Test M1 – Descriptive Statistics (Chapters 1–5)

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SSC CGL Statistics – Mock Test M1 – Descriptive Statistics (Chapters 1–5) – 25 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.  
In an inclusive classification of whole-number data, the class 20–24 has class boundaries:

Correct Answer: A [19.5 and 24.5]

Explanation:

Half the gap of 1 between 24 and 25 is subtracted below and added above: 19.5 and 24.5.

2.  
A family spends ₹ 4,800 on rent out of a monthly budget of ₹ 28,800. In a pie diagram of the budget, the rent sector has angle:

Correct Answer: B [60°]

Explanation:

Answer: 60°. 4,800/28,800 × 360° = 60°.

3.  
Where the less-than and more-than ogives of a distribution of N items cross, the x-coordinate and the y-coordinate are respectively:

Correct Answer: D [the median and N/2]

Explanation:

At the crossing both cumulative frequencies equal N/2, so x is the median.

4.  
A student scores 60, 75 and 90 in three papers carrying weights 2, 3 and 5. The weighted mean score is:

Correct Answer: C [79.5]

Explanation:

(120 + 225 + 450)/10 = 795/10 = 79.5.

5.  
Section A has 40 students with mean mark 52 and section B has 60 students with mean mark 47. The mean mark of all 100 students is:

Correct Answer: A [49]

Explanation:

Answer: 49. (2,080 + 2,820)/100 = 49.

6.  
The mean of 20 observations was found to be 45. Later it was noticed that 63 had been copied as 36. The correct mean is:

Correct Answer: D [46.35]

Explanation:

Total rises by 27 → mean rises by 27/20 = 1.35 → 46.35.

7.  
The arithmetic mean and geometric mean of two positive numbers are 15 and 12. Their harmonic mean is:

Correct Answer: C [9.6]

Explanation:

For two numbers GM² = AM × HM → HM = 144/15 = 9.6.

8.  
The geometric mean of 3, 12 and 48 is:

Correct Answer: B [12]

Explanation:

Answer: 12. ∛(3 × 12 × 48) = ∛1728 = 12.

9.  

Directions (Q 9–10): Marks of 40 candidates – 0–10: 5, 10–20: 8, 20–30: 12, 30–40: 9, 40–50: 6.

The median mark is (to two decimals):

Correct Answer: C [25.83]

Explanation:

N/2 = 20; median class 20–30 (cf before it 13): 20 + (20 − 13)/12 × 10 = 25.83.

10.  
(Use the directions above – Q 9–10)
The mode (by the interpolation formula, to two decimals) is:

Correct Answer: D [25.71]

Explanation:

Modal class 20–30: 20 + (12 − 8)/[(12 − 8) + (12 − 9)] × 10 = 20 + 40/7 = 25.71.

11.  
For the 11 values 3, 5, 7, 8, 10, 12, 15, 18, 20, 22, 25, the quartile deviation (quartiles by the (n + 1) rule) is:

Correct Answer: A [6.5]

Explanation:

Q₁ = 3rd value = 7, Q₃ = 9th value = 20 → QD = (20 − 7)/2 = 6.5.

12.  
Five readings 4, 7, 10, 13 and 16 are taken. Their standard deviation is:

Correct Answer: B [3√2 ≈ 4.24]

Explanation:

Deviations −6, −3, 0, 3, 6; Σd² = 90; σ² = 90/5 = 18 → σ = 3√2.

13.  
Series A: mean 40, SD 8. Series B: mean 60, SD 9. Which statement is correct?

Correct Answer: D [B is more consistent (CV 15% against 20%)]

Explanation:

CV(A) = 8/40 = 20%, CV(B) = 9/60 = 15%; the smaller CV is more consistent.

14.  
The SD of x is 4. What is the variance of y = 3x − 5?

Correct Answer: B [144]

Explanation:

σᵧ = |3| × 4 = 12 → variance 144; the −5 has no effect.

15.  
Group 1: 20 values, mean 30, SD 4. Group 2: 30 values, mean 35, SD 6. The variance of the combined 50 values is:

Correct Answer: A [34]

Explanation:

Combined mean 33; d₁ = −3, d₂ = 2; σ² = [20(16 + 9) + 30(36 + 4)]/50 = 1700/50 = 34.

16.  
The mean deviation about the mean of 4, 8, 10, 14, 19 is:

Correct Answer: C [4.4]

Explanation:

Mean 11; |deviations| 7, 3, 1, 3, 8 → 22/5 = 4.4.

17.  
About A = 3 the first three raw moments of a distribution are 1, 6 and 10. The third central moment μ₃ is:

Correct Answer: C [-6]

Explanation:

μ₃ = 10 − 3(6)(1) + 2(1)³ = 10 − 18 + 2 = −6.

18.  
A distribution has μ₂ = 5 and μ₄ = 60. Its kurtosis is:

Correct Answer: D [platykurtic (β₂ = 2.4)]

Explanation:

Answer: platykurtic (β₂ = 2.4). β₂ = 60/25 = 2.4 < 3.

19.  
Two-quantity comparisonOne series has mean 70, mode 64 and SD 15; another has Q₁ = 18, Md = 24 and Q₃ = 26:
Quantity I: Karl Pearson's coefficient of skewness of the first series
Quantity II: Bowley's coefficient of skewness of the second series

Correct Answer: A [Quantity I > Quantity II]

Explanation:

QI = (70 − 64)/15 = 0.4; QII = (26 + 18 − 48)/(26 − 18) = −0.5.

20.  
Cov(x, y) = 18, Var(x) = 16 and Var(y) = 36. Karl Pearson's coefficient of correlation is:

Correct Answer: B [0.75]

Explanation:

Answer: 0.75. 18/(4 × 6) = 0.75.

21.  
The two regression coefficients are 1.6 and 0.4. The coefficient of correlation is:

Correct Answer: A [0.8]

Explanation:

r = √(1.6 × 0.4) = √0.64 = 0.8.

22.  
Find the correlation coefficient implied by the pair of regression lines 2x + 3y = 27 and x + 6y = 36.

Correct Answer: A [−0.5]

Explanation:

Taking 2x + 3y = 27 as y on x gives byx = −2/3 and bxy = −6 (product 4 > 1, impossible).

23.  
For 7 pairs of ranks the sum of squared rank differences is 14. Spearman's rank correlation coefficient is:

Correct Answer: D [0.75]

Explanation:

1 − 6 × 14/(7 × 48) = 1 − 84/336 = 0.75.

24.  
In a 2 × 2 table of two attributes, (AB) = 35, (Aβ) = 15, (αB) = 25 and (αβ) = 25. Yule's coefficient of association is:

Correct Answer: B [0.4]

Explanation:

(875 − 375)/(875 + 375) = 500/1250 = 0.4.

25.  
For three variables with r₁₂ = 0.4 and r₁₃ = r₂₃ = 0.2, what is the correlation between x₁ and x₂ after the effect of x₃ is removed?

Correct Answer: C [0.38]

Explanation:

(0.4 − 0.04)/√(0.96 × 0.96) = 0.36/0.96 = 0.375.

➤ 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

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