SSC CGL Statistics – Mock Test M3 – Mixed Paper II Set (All 12 Chapters)
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Answer: 140. 175/125 × 100 = 140.
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SSC CGL Statistics – Mock Test M3 – Mixed Paper II Set (All 12 Chapters) – 50 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.
Figures an investigator obtains by conducting his own household survey are:
Correct Answer: C [primary data]
Explanation:
First-hand data collected for the present purpose are primary.
2.
In a histogram with standard class width 10, the class 20–40 has frequency 30. The adjusted height of its rectangle is:
Correct Answer: B [15]
Explanation:
Width 20 is twice the standard → height 30/2 = 15.
3.
Statement-basedWhich of the following is/are correct?
I. A table's stub gives the row headings.
II. A histogram can be drawn for a distribution with unequal classes only after adjusting the heights.
I. A table's stub gives the row headings.
II. A histogram can be drawn for a distribution with unequal classes only after adjusting the heights.
Correct Answer: D [Both I and II]
Explanation:
The stub holds row captions; unequal widths need frequency densities.
4.
The median of 14, 9, 22, 17, 11, 25 is:
Correct Answer: A [15.5]
Explanation:
Sorted 9, 11, 14, 17, 22, 25 → (14 + 17)/2 = 15.5.
5.
For a moderately skewed distribution the mean is 45 and the median is 42. By the empirical relation the mode is:
Correct Answer: A [36]
Explanation:
Answer: 36. Mode = 3 × 42 − 2 × 45 = 36.
6.
For the 19 values 10, 20, 30, …, 190 (deciles by the (n + 1) rule), the third decile D₃ is:
Correct Answer: C [60]
Explanation:
Position 3 × 20/10 = 6 → 6th value = 60.
7.
The sum of the squares of the deviations of a set of values is the least when the deviations are measured from the:
Correct Answer: B [arithmetic mean]
Explanation:
Σ(x − a)² = Σ(x − x̄)² + n(x̄ − a)² is smallest at a = x̄.
8.
The largest value of a data set is 80 and the smallest is 20. The coefficient of range is:
Correct Answer: D [0.6]
Explanation:
Answer: 0.6. (80 − 20)/(80 + 20) = 0.6.
9.
The variance of the first ten natural numbers is:
Correct Answer: A [8.25]
Explanation:
Answer: 8.25. (n² − 1)/12 = 99/12 = 8.25.
10.
Q₁ = 30 and Q₃ = 50. The coefficient of quartile deviation is:
Correct Answer: B [0.25]
Explanation:
Answer: 0.25. (50 − 30)/(50 + 30) = 0.25.
11.
Each value of a data set with SD 7 is multiplied by −2 and then 5 is added. The new SD is:
Correct Answer: C [14]
Explanation:
SD is multiplied by |−2| = 2; adding 5 has no effect.
12.
In a symmetric distribution, which of these is necessarily zero?
Correct Answer: D [the third central moment μ₃]
Explanation:
All odd central moments vanish for a symmetric distribution.
13.
A distribution has γ₂ = −0.4. Its β₂ and type of kurtosis are:
Correct Answer: D [2.6, platykurtic]
Explanation:
Answer: 2.6, platykurtic. β₂ = γ₂ + 3 = 2.6 < 3.
14.
About A = 10 the first two raw moments are 2 and 13. The standard deviation is:
Correct Answer: A [3]
Explanation:
Answer: 3. μ₂ = 13 − 4 = 9 → SD = 3.
15.
Mean 30, median 32 and SD 10. Karl Pearson's coefficient of skewness (median form) is:
Correct Answer: B [−0.6]
Explanation:
Answer: −0.6. 3(30 − 32)/10 = −0.6.
16.
Given σᵧ = 10, σₓ = 5 and a correlation of 0.6, what is the slope of the line used to predict y from x?
Correct Answer: C [1.2]
Explanation:
Answer: 1.2. byx = 0.6 × 10/5 = 1.2.
17.
If the two lines of regression are perpendicular to each other, the coefficient of correlation is:
Correct Answer: A [0]
Explanation:
Perpendicular lines y = ȳ and x = x̄ arise only when r = 0.
18.
Two judges rank 9 entries and the squared rank differences add up to 30. What is the rank correlation between the judges?
Correct Answer: C [0.75]
Explanation:
Answer: 0.75. 1 − 180/720 = 0.75.
19.
The coefficient of determination for a correlation of −0.7 is:
Correct Answer: D [0.49]
Explanation:
r² = (−0.7)² = 0.49; the sign of r does not matter.
20.
Two fair dice are rolled. The probability that the sum is at least 10 is:
Correct Answer: B [1/6]
Explanation:
Sums 10, 11, 12: 3 + 2 + 1 = 6 ways → 6/36.
21.
Events A and B cannot occur together; P(A) = 0.5 and P(B) = 0.3. What is the probability that neither occurs?
Correct Answer: C [0.2]
Explanation:
Answer: 0.2. 1 − (0.5 + 0.3) = 0.2.
22.
Three balls are taken out at once from a box of 5 red and 5 green balls. What is the chance that all three are red?
Correct Answer: D [1/12]
Explanation:
C(5, 3)/C(10, 3) = 10/120 = 1/12.
23.
Machine P makes 60% and machine Q 40% of the output; 1% of P's and 3% of Q's items are defective. A defective item is found. The probability that Q made it is:
Correct Answer: A [2/3]
Explanation:
Answer: 2/3. 0.012/(0.006 + 0.012) = 2/3.
24.
The expected value of the number shown by a fair die is:
Correct Answer: B [3.5]
Explanation:
(1 + 2 + … + 6)/6 = 21/6 = 3.5.
25.
X is binomial with n = 5 and p = 0.2. P(X = 0) is:
Correct Answer: A [0.32768]
Explanation:
Answer: 0.32768. (0.8)⁵ = 0.32768.
26.
X is normal with mean 100 and SD 15. The standard score of x = 130 is:
Correct Answer: D [2]
Explanation:
Answer: 2. z = (130 − 100)/15 = 2.
27.
Assertion–Reason
A: For a Poisson distribution the mean and the variance are equal.
R: A Poisson distribution is always symmetric.
A: For a Poisson distribution the mean and the variance are equal.
R: A Poisson distribution is always symmetric.
Correct Answer: B [A is true but R is false]
Explanation:
Mean = variance = m is true; the Poisson is positively skewed (β₁ = 1/m), so R is false.
28.
Which statement about errors is correct?
Correct Answer: C [Non-sampling errors can occur in a census as well as in a sample survey]
Explanation:
Non-sampling errors (response, recording, processing) occur in any enquiry; sampling error exists only when a sample is used.
29.
In which of these methods are the selection probabilities of the units unknown?
Correct Answer: C [Quota sampling]
Explanation:
In quota sampling the interviewer chooses the units – no known selection probabilities.
30.
A sample of 96 gives a proportion p = 0.4. The standard error of the proportion is:
Correct Answer: D [0.05]
Explanation:
√(0.4 × 0.6/96) = √(1/400) = 0.05 (0.0025 forgets the square root).
31.
To halve the standard error of the sample mean (simple random sampling, large population), the sample size must be:
Correct Answer: B [multiplied by 4]
Explanation:
Answer: multiplied by 4. SE ∝ 1/√n.
32.
A sample has the values 2, 4, 6, 8. The unbiased estimate of the population variance is:
Correct Answer: A [20/3 ≈ 6.67]
Explanation:
x̄ = 5; Σ(x − x̄)² = 20; s² = 20/3 ≈ 6.67.
33.
The probability of a Type II error of a test is 0.15. The power of the test is:
Correct Answer: D [0.85]
Explanation:
Answer: 0.85. Power = 1 − β = 0.85.
34.
In a sample of 100 voters, 50 favour a proposal. The 95% confidence interval for the population proportion (z = 1.96) is:
Correct Answer: A [0.402 to 0.598]
Explanation:
0.5 ± 1.96 × √(0.25/100) = 0.5 ± 0.098.
35.
Two samples have unbiased variances 24 and 8. The F statistic for testing equality of population variances is:
Correct Answer: C [3]
Explanation:
Larger over smaller: 24/8 = 3.
36.
In a one-way ANOVA of 30 observations, the total degrees of freedom are:
Correct Answer: B [29]
Explanation:
Answer: 29. N − 1 = 29.
37.
In an ANOVA table SS within = 84 with 21 degrees of freedom. The mean square within (MSE) is:
Correct Answer: A [4]
Explanation:
Answer: 4. 84/21 = 4.
38.
A one-way ANOVA of 33 observations in 3 groups has total SS = 150 and between-groups SS = 60. The F ratio is:
Correct Answer: C [10]
Explanation:
SSE = 90; MSB = 60/2 = 30; MSE = 90/30 = 3; F = 10.
39.
In analysis of variance the F ratio compares:
Correct Answer: B [the between-groups mean square with the within-groups mean square]
Explanation:
Answer: the between-groups mean square with the within-groups mean square. F = MSB/MSE.
40.
The 3-yearly moving averages of 12, 15, 18, 24, 30 are:
Correct Answer: D [15, 19, 24]
Explanation:
(12 + 15 + 18)/3 = 15; (15 + 18 + 24)/3 = 19; (18 + 24 + 30)/3 = 24.
41.
Sales for five years (coded x = −2, −1, 0, 1, 2) are 8, 11, 13, 16, 22. The least-squares trend value for the next year (x = 3) is:
Correct Answer: D [23.9]
Explanation:
a = 70/5 = 14; b = Σxy/Σx² = 33/10 = 3.3; ŷ = 14 + 3.3 × 3 = 23.9.
42.
Higher sales of woollen clothes every winter, year after year, are an example of:
Correct Answer: B [seasonal variation]
Explanation:
A pattern that repeats within a year is seasonal.
43.
In the multiplicative model of a time series the observed value Y is written as:
Correct Answer: A [T × S × C × I]
Explanation:
Multiplicative model Y = T × S × C × I.
44.
The quarterly averages of a series are 45, 60, 75 and 60. By the method of simple averages, the seasonal index of the first quarter is:
Correct Answer: C [75]
Explanation:
Grand average = 60; index = 45/60 × 100 = 75.
45. Laspeyres' price index (to two decimals) is:
Directions (Q 45–47): Two items – Base year prices 10 and 20 with quantities 5 and 4; current year prices 12 and 25 with quantities 6 and 2.
Correct Answer: C [123.08]
Explanation:
Σp₁q₀/Σp₀q₀ × 100 = 160/130 × 100 = 123.08.
46.
(Use the directions above – Q 45–47)
What is the price index that uses current-year quantities as weights (Paasche)?
What is the price index that uses current-year quantities as weights (Paasche)?
Correct Answer: D [122.00]
Explanation:
Σp₁q₁/Σp₀q₁ × 100 = 122/100 × 100 = 122.
47.
(Use the directions above – Q 45–47)
Fisher's ideal price index (to two decimals) is:
Fisher's ideal price index (to two decimals) is:
Correct Answer: B [122.54]
Explanation:
Paasche = 122/100 × 100 = 122; Fisher = √(123.08 × 122) ≈ 122.54.
48.
Which index number satisfies both the time reversal test and the factor reversal test?
Correct Answer: A [Fisher's ideal index]
Explanation:
Fisher's index meets both tests.
49.
Deflate a monthly salary of ₹ 22,500 by a cost of living index of 125 (base 100). The salary in base-year rupees is:
Correct Answer: D [₹ 18,000]
Explanation:
Answer: ₹ 18,000. 22,500 × 100/125 = ₹ 18,000.
50.
On the old base, the index for 2020 is 125 and for 2024 is 175. Shifted to the new base 2020 = 100, the 2024 index is:
Correct Answer: C [140]
Explanation:
Answer: 140. 175/125 × 100 = 140.
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📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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