SSC CGL Mock – Paper II Statistics Mock Test 02 – Paper II · Statistics | Online Quiz

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SSC CGL Mock – Paper II Statistics Mock Test 02 – Paper II · Statistics – 100 questions, subject: Full Mock Tests. 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.

Enumerators go from house to house, ask the questions and write the answers themselves on the form. Such a form is called a

Correct Answer: A [schedule]

Explanation:

A schedule is filled in by the enumerator; a questionnaire is filled in by the informant.

Which one of these characteristics can take only separate, countable values (and is therefore discrete)?

Correct Answer: C [Number of rooms in a house]

Explanation:

A discrete variable takes only separate (countable) values; height, time and weight are continuous.

Diagram-basedThe 'less than' ogive of a fictional test is shown; the labels give the cumulative frequencies.

How many students scored from 30 to less than 40 marks?

Correct Answer: D [18]

Explanation:

Frequency of 30–40 = cf(40) − cf(30) = 46 − 28 = 18.

The classes 120–139, 140–159, 160–179 are made continuous (exclusive). The second class then becomes

Correct Answer: B [139.5–159.5]

Explanation:

Half the gap (1/2 × 1 = 0.5) is taken from every lower limit and added to every upper limit.

The populations of two fictional towns, 2,500 and 6,400, are shown by circles whose areas are in proportion to the populations. If the first circle has radius 3 cm, the radius of the second is

Correct Answer: D [4.8 cm]

Explanation:

Radius ∝ √value: 3 × √(6400/2500) = 3 × 1.6 = 4.8 cm.

Two families with very different incomes are to be compared on the share of food, rent, education and other items in their spending. The most suitable diagram is the

Correct Answer: A [percentage sub-divided bar diagram]

Explanation:

Each bar is made 100 and divided by percentages, so shares compare fairly even when totals differ.

In a histogram with unequal classes, heights are adjusted to a standard width of 10. The class 20–50 has frequency 45. Its adjusted height is

Correct Answer: B [15]

Explanation:

Answer: 15. Height = 45 × 10/30 = 15.

Before using secondary data, an investigator should mainly examine whether the data are

Correct Answer: C [reliable, suitable and adequate for the enquiry]

Explanation:

Secondary data must be checked for reliability, suitability and adequacy before use.

Time taken (minutes) by 40 employees of a fictional office to reach work: 10–20: 4, 20–30: 9, 30–40: 14, 40–50: 8, 50–60: 5. The median travel time is

Correct Answer: C [35]

Explanation:

N/2 = 20; median class 30–40 (cf before = 13): 30 + (20 − 13)/14 × 10 = 35.

10.

Heights (cm) of 56 saplings in a fictional nursery: 0–10: 5, 10–20: 12, 20–30: 20, 30–40: 13, 40–50: 6. Using the interpolation formula, the modal height is

Correct Answer: A [25.33]

Explanation:

Modal class 20–30: 20 + (20 − 12)/(2×20 − 12 − 13) × 10 = 20 + 8/15 × 10 = 25.33.

11.

Using the (n + 1) rule, find the upper quartile Q₃ of the fictional data 14, 17, 21, 22, 25, 28, 30, 33, 36, 41.

Correct Answer: D [33.75]

Explanation:

Position = 3(n + 1)/4 = 8.25; Q₃ = 33 + 0.25 × (36 − 33) = 33.75.

12.

The mean of 6, 9, x, 15 and 18 is 13. The value of x is

Correct Answer: B [17]

Explanation:

Total = 5 × 13 = 65; x = 65 − 48 = 17.

13.

For two positive numbers, the arithmetic mean is 50 and the geometric mean is 40. Their harmonic mean is

Correct Answer: B [32]

Explanation:

For two numbers G² = A × H, so H = 40²/50 = 32.

14.

A fictional town's population grew by different percentages in successive decades. To find the average rate of growth per decade, the right average is the

Correct Answer: A [geometric mean]

Explanation:

Growth compounds (rates multiply), so the geometric mean of the growth factors is used.

15.

Fill in the blankThe sum of absolute deviations Σ|x − A| of a set of values is the least when A is the

Correct Answer: D [median]

Explanation:

The mean minimises Σ(x − A)²; the median minimises Σ|x − A|.

16.

The marks of a fictional class have mean 40 and median 38. Each mark is tripled and then 5 marks are deducted from every student. The median of the revised marks is

Correct Answer: C [109]

Explanation:

Median follows the same change: 3 × 38 − 5 = 109.

17.

A candidate's score is at the 90th percentile of all the scores in a fictional test. This means that

Correct Answer: C [about 90% of the candidates scored less than this score]

Explanation:

P₉₀ is the value below which about 90% of the observations lie.

18.

What is the mean of the 50 consecutive whole numbers 101, 102, 103, …, 150?

Correct Answer: D [125.5]

Explanation:

Mean of an AP = (first + last)/2 = (101 + 150)/2 = 125.5.

19.

Two fictional sections of a class: 40 students with mean 50 and SD 6, and 60 students with mean 55 and SD 8. The SD of all 100 students together is

Correct Answer: A [7.67]

Explanation:

Combined mean 53; σ² = [40(36 + 9) + 60(64 + 4)]/100 = 58.8; σ ≈ 7.67.

20.

The SD of a variable x is 4. If y = (3x − 5)/2, the SD of y is

Correct Answer: B [6]

Explanation:

SD ignores the −5 (origin) and is multiplied by |3/2| (scale): 4 × 3/2 = 6.

21.

A fictional shop records the number of customers in each of 10 hours: Σx = 70 and Σx² = 580. Dividing by n, the variance of the hourly count is

Correct Answer: B [9]

Explanation:

σ² = Σx²/n − (Σx/n)² = 58 − 49 = 9.

22.

The mean deviation about the median of the fictional values 2, 5, 6, 9, 13, 16, 19 is

Correct Answer: D [5]

Explanation:

Median 9; |x − 9| = 7, 4, 3, 0, 4, 7, 10 → 35/7 = 5.

23.

For a fictional data set, Q₁ = 35 and the coefficient of quartile deviation is 0.2. Q₃ is

Correct Answer: A [52.5]

Explanation:

(Q₃ − 35)/(Q₃ + 35) = 0.2 → 0.8 Q₃ = 1.2 × 35 → Q₃ = 52.5.

24.

Fill in the blankThe root-mean-square deviation Σ(x − A)²/n, square-rooted, is the least when A is the

Correct Answer: C [arithmetic mean]

Explanation:

Σ(x − A)² = Σ(x − x̄)² + n(x̄ − A)², least when A = x̄; this least value is the SD.

25.

The coefficient of variation of a fictional series is 25% and its SD is 12. Its mean is

Correct Answer: B [48]

Explanation:

x̄ = σ × 100/CV = 12 × 100/25 = 48.

26.

Lengths of nails from a fictional machine are normally distributed with SD 15 mm. Using the rule QD ≈ (2/3)σ, the semi-interquartile range in mm is about

Correct Answer: D [10]

Explanation:

Answer: 10. QD ≈ (2/3) × 15 = 10.

27.

Fill in the blankIn a Lorenz diagram, the farther the Lorenz curve lies from the line of equal distribution, the

Correct Answer: C [greater is the inequality]

Explanation:

The diagonal shows perfect equality; a curve bulging away from it shows greater inequality.

28.

For the number of complaints a day at a fictional help desk, μ₁′ = 1, μ₂′ = 5 and μ₃′ = 20 (moments about zero). The third moment about the mean is

Correct Answer: A [7]

Explanation:

μ₃ = μ₃′ − 3μ₂′μ₁′ + 2(μ₁′)³ = 20 − 15 + 2 = 7.

29.

For a fictional distribution μ₂ = 5 and μ₄ = 100. The distribution is

Correct Answer: A [leptokurtic (β₂ = 4)]

Explanation:

β₂ = μ₄/μ₂² = 100/25 = 4 > 3 → leptokurtic.

30.

Rents (₹ hundred) in a fictional locality have mean 60, median 63 and SD 15. Using the median, Karl Pearson's skewness 3(mean − median)/σ is

Correct Answer: D [−0.6]

Explanation:

Answer: −0.6. 3(60 − 63)/15 = −0.6.

31.

Statement-basedConsider the statements:
I. When every observation is multiplied by a constant k, the r-th central moment is multiplied by k^r.
II. Raw moments about the origin do not change when a constant is added to every observation.
Which statement(s) is/are correct?

Correct Answer: A [Only I]

Explanation:

x − x̄ becomes k(x − x̄), so μᵣ becomes k r μᵣ; raw moments about 0 do change with a shift.

32.

A distribution has β₂ = 2.4. Its excess kurtosis γ₂ = β₂ − 3 is

Correct Answer: C [−0.6]

Explanation:

γ₂ = 2.4 − 3 = −0.6 (negative → platykurtic).

33.

Whatever the data, the quartile-based (Bowley) measure of skewness can only take values in the range

Correct Answer: B [−1 and +1]

Explanation:

|Q₃ + Q₁ − 2Md| can never exceed Q₃ − Q₁, so the coefficient lies in [−1, 1].

34.

For a normal distribution with standard deviation 2, the fourth central moment μ₄ is

Correct Answer: B [48]

Explanation:

Normal: β₂ = 3, so μ₄ = 3σ⁴ = 3 × 16 = 48.

35.

Find Karl Pearson's correlation coefficient for the fictional pairs (x, y): (1, 2), (2, 4), (3, 5), (4, 4), (5, 5).

Correct Answer: D [0.77]

Explanation:

Σdx dy = 6, Σdx² = 10, Σdy² = 6; r = 6/√60 ≈ 0.77.

36.

A fictional shop links advertising spend x (₹ thousand) and sales y (₹ lakh): x̄ = 10, ȳ = 20, σₓ = 2, σᵧ = 5, r = 0.4. The predicted sales (₹ lakh) for an advertising spend of 14 are

Correct Answer: C [24]

Explanation:

bᵧₓ = 0.4 × 5/2 = 1; y = 20 + 1(14 − 10) = 24.

37.

Price x and daily demand y of a fictional snack give the regression lines 3x + 2y = 26 and 6x + y = 31. Find Karl Pearson's r between price and demand.

Correct Answer: A [−0.5]

Explanation:

Taking 3x + 2y = 26 as y on x: bᵧₓ = −3/2; 6x + y = 31 as x on y: bₓᵧ = −1/6; product 1/4 ≤ 1 (the other way gives 4 > 1).

38.

For a sample of 64 pairs, r = 0.6. The probable error of r, 0.6745 (1 − r²)/√n, is

Correct Answer: D [0.0540]

Explanation:

PE = 0.6745 × (1 − 0.36)/8 = 0.6745 × 0.08 = 0.0540.

39.

Marks of six fictional students in Statistics: 56, 48, 48, 62, 70, 41; in Economics: 60, 52, 58, 59, 72, 50. Spearman's rank correlation (with the correction for the tie) is

Correct Answer: C [0.91]

Explanation:

Statistics ranks (highest = 1): 3, 4.5, 4.5, 2, 1, 6; Economics ranks: 2, 5, 4, 3, 1, 6; Σd² = 2.5, correction (2³ − 2)/12 = 0.5; ρ = 1 − 6(2.5 + 0.5)/210 ≈ 0.91.

40.

Statement-basedConsider the statements:
I. The correlation coefficient does not change if every x is replaced by (x − 20)/4.
II. The regression coefficient bᵧₓ does not change when the unit of y is changed from rupees to paise.
Which statement(s) is/are correct?

Correct Answer: A [Only I]

Explanation:

r is unaffected by origin and positive scale; bᵧₓ = r σᵧ/σₓ changes with the scale of y (×100 here).

41.

In a fictional study, X₁ = wheat yield, X₂ = fertiliser used and X₃ = rainfall, with r₁₂ = 0.7, r₁₃ = 0.5 and r₂₃ = 0.5. Eliminating the effect of rainfall, the correlation of yield with fertiliser (r₁₂.₃) is

Correct Answer: A [0.6]

Explanation:

(r₁₂ − r₁₃r₂₃)/√((1 − r₁₃²)(1 − r₂₃²)) = (0.7 − 0.25)/0.75 = 0.6.

42.

In a 2 × 2 table of attributes, the class frequency (AB) is zero while all the other cells are non-zero. Yule's coefficient Q is

Correct Answer: B [−1]

Explanation:

Q = (0 × d − bc)/(0 × d + bc) = −bc/bc = −1: perfect disassociation.

43.

The two lines of regression coincide (become one line) when

Correct Answer: D [r = +1 or r = −1]

Explanation:

With |r| = 1 both lines are the same straight line; with r = 0 they are perpendicular.

44.

For 10 pairs of fictional values, Σx = 50, Σy = 80 and Σxy = 460. The covariance (divide by n) is

Correct Answer: A [6]

Explanation:

Cov = Σxy/n − x̄ȳ = 46 − 5 × 8 = 6.

45.

The points of a scatter diagram form a wide horizontal band with no upward or downward trend. The correlation coefficient is likely to be

Correct Answer: C [close to 0]

Explanation:

No trend in the cloud → no linear relation → r near zero.

46.

In a fictional dice game, a player wins a point when the product of the numbers on two fair dice is even. The chance of winning a point on one roll is

Correct Answer: B [3/4]

Explanation:

Product is odd only when both are odd: 9/36; P(even) = 1 − 1/4 = 3/4.

47.

A calendar year of 365 days is picked at random. What is the chance that this year contains fifty-three Mondays?

Correct Answer: A [1/7]

Explanation:

365 days = 52 weeks + 1 day; that extra day must be a Monday: 1/7.

48.

In a fictional game, a fair coin decides which of two jars is used: jar I (3 green, 2 yellow marbles) or jar II (2 green, 3 yellow). One marble taken from the chosen jar is green. The chance that jar I was used is

Correct Answer: D [3/5]

Explanation:

Bayes: (½ × 3/5)/(½ × 3/5 + ½ × 2/5) = 3/5.

49.

Machine A makes 60% and machine B makes 40% of the output of a fictional factory; 2% of A's and 5% of B's items are defective. The probability that a randomly chosen item is defective is

Correct Answer: C [0.032]

Explanation:

Total probability: 0.6 × 0.02 + 0.4 × 0.05 = 0.012 + 0.020 = 0.032.

50.

Two fictional students try a puzzle independently; their chances of solving it are 1/3 and 1/4. The probability that the puzzle is solved is

Correct Answer: B [1/2]

Explanation:

P(at least one) = 1 − (2/3)(3/4) = 1 − 1/2 = 1/2.

51.

In a fictional colony, 50% of homes own a car (A), 40% a scooter (B) and 30% a bicycle (C); 20% own A and B, 10% B and C, 10% C and A, and 5% all three. The probability that a home owns at least one of them is

Correct Answer: D [0.85]

Explanation:

0.5 + 0.4 + 0.3 − 0.2 − 0.1 − 0.1 + 0.05 = 0.85.

52.

A fictional residents' association picks a 3-member panel by lottery from 4 men and 3 women. The chance that the panel has exactly two women is

Correct Answer: A [12/35]

Explanation:

C(3,2) × C(4,1)/C(7,3) = 12/35.

53.

Statement-basedConsider the statements:
I. If A and B are independent and P(B) > 0, then P(A | B) = P(A).
II. Two mutually exclusive events with positive probabilities are always independent.
Which statement(s) is/are correct?

Correct Answer: A [Only I]

Explanation:

II is wrong: for such events P(A ∩ B) = 0 ≠ P(A)P(B) > 0, so they are dependent.

54.

Odd one outFor the sample space S = {a, b, c}, which assignment of probabilities (to a, b, c) is NOT valid?

Correct Answer: C [0.6, 0.5, −0.1]

Explanation:

Every probability must be ≥ 0 (and the total 1); −0.1 breaks the first axiom.

55.

Two cards are drawn at random together from a pack of 52. The probability that both are hearts is

Correct Answer: B [1/17]

Explanation:

C(13,2)/C(52,2) = 78/1326 = 1/17.

56.

For a fictional discrete variable, P(X = x) = kx² for x = 1, 2, 3. The probability P(X ≥ 2) is

Correct Answer: D [13/14]

Explanation:

k(1 + 4 + 9) = 1 → k = 1/14; P(X ≥ 2) = (4 + 9)/14 = 13/14.

57.

The number of rooms X booked per enquiry at a fictional guest-house takes values 1, 2, 3 with probabilities 1/4, 1/2, 1/4. Var(X) is

Correct Answer: A [0.5]

Explanation:

E(X) = 2; E(X²) = 1/4 + 2 + 9/4 = 4.5; Var = 4.5 − 4 = 0.5.

58.

The number of successful hits by a fictional bowler in a match follows a binomial distribution with mean 8 and variance 4.8. The number of trials n is

Correct Answer: B [20]

Explanation:

q = variance/mean = 0.6; p = 0.4; n = mean/p = 20.

59.

Three fictional seeds are sown; each fails to sprout with probability 0.2, independently. The probability that at least one fails is

Correct Answer: C [0.488]

Explanation:

1 − (0.8)³ = 1 − 0.512 = 0.488.

60.

Typing errors per page in a fictional report follow a Poisson law, and pages with exactly one error are as common as pages with exactly two. The mean number of errors per page is

Correct Answer: C [2]

Explanation:

Answer: 2. e⁻ᵐ m = e⁻ᵐ m²/2 → m = 2.

61.

Fill in the blankFor a normal distribution, about 95% of the values lie within

Correct Answer: B [μ ± 1.96σ]

Explanation:

Area between −1.96 and +1.96 is 0.95; ±2.58 gives 0.99.

62.

Heights of fictional plants are normal with mean 60 cm and SD 8 cm. Given Φ(1.5) = 0.9332 and Φ(0.75) = 0.7734, the proportion of plants between 54 cm and 72 cm is

Correct Answer: A [0.7066]

Explanation:

z = −0.75 and 1.5; 0.9332 − (1 − 0.7734) = 0.7066.

63.

Waiting time (minutes) at a fictional ticket window is exponential with λ = 0.5 per minute. Using e⁻¹ = 0.3679, the probability of waiting more than 2 minutes is

Correct Answer: D [0.3679]

Explanation:

P(X > 2) = e −0.5 × 2 = e⁻¹ = 0.3679.

64.

A fictional random variable has density f(x) = kx for 0 ≤ x ≤ 2 (zero elsewhere). Its mean E(X) is

Correct Answer: A [4/3]

Explanation:

∫₀² kx dx = 2k = 1 → k = 1/2; E(X) = ∫₀² x · x/2 dx = 8/6 = 4/3.

65.

At a fictional café, X = 1 if a customer orders tea (else 0) and Y = 1 if she orders a snack (else 0); P(0, 0) = 0.12, P(0, 1) = 0.18, P(1, 0) = 0.28, P(1, 1) = 0.42. Which statement is correct?

Correct Answer: D [X and Y are independent, since every P(x, y) = P(x) P(y)]

Explanation:

P(X = 0) = 0.3, P(X = 1) = 0.7; P(Y = 0) = 0.4, P(Y = 1) = 0.6; e.g.

66.

By Chebyshev's inequality, the probability that any random variable lies within 2 standard deviations of its mean is at least

Correct Answer: C [3/4]

Explanation:

P(|X − μ| < kσ) ≥ 1 − 1/k² = 1 − 1/4 = 3/4.

67.

Two cards are drawn one by one with replacement from 5 numbered cards (order counted). The number of possible samples is

Correct Answer: B [25]

Explanation:

With replacement: N n = 5² = 25.

68.

A fictional poll finds that 40% of 96 randomly chosen households own a two-wheeler. Estimate the standard error of this sample proportion.

Correct Answer: D [0.05]

Explanation:

SE = √(pq/n) = √(0.4 × 0.6/96) = √0.0025 = 0.05.

69.

Stratified random sampling is most useful when the population

Correct Answer: B [is heterogeneous but can be split into fairly homogeneous groups]

Explanation:

Strata are made internally alike; sampling every stratum gives a more precise estimate.

70.

In which of these cases is a complete enumeration (census) the right choice rather than a sample?

Correct Answer: A [Preparing the list of all voters of a constituency]

Explanation:

A voters' list must include every voter; the other tests are destructive or need only a sample.

71.

A fictional survey team is told to interview exactly 30 men and 20 women in a market but may choose the persons itself. This is

Correct Answer: C [quota sampling]

Explanation:

Fixed quotas filled by the interviewer's choice (not at random) – quota sampling.

72.

A fictional agency wants to estimate a mean within ±2 units with 95% confidence (z = 1.96). If σ = 10, the minimum sample size is

Correct Answer: C [97]

Explanation:

n = (zσ/E)² = (1.96 × 10/2)² = 96.04 → round up to 97.

73.

Statement-basedConsider the statements:
I. Non-sampling errors can occur even in a complete census.
II. Sampling error can be reduced by taking a larger random sample.
Which statement(s) is/are correct?

Correct Answer: C [Both I and II]

Explanation:

Non-sampling errors (wrong answers, coding slips) affect censuses too; SE falls as n grows.

74.

For a test, the probability of a Type II error at a particular alternative is 0.2. The power of the test at that alternative is

Correct Answer: B [0.8]

Explanation:

Power = 1 − β = 1 − 0.2 = 0.8.

75.

A sample of 16 fictional bags gives mean weight 52 kg and sample SD s = 5 kg. To test H₀: μ = 50 (two-sided, 5%) with t₀.₀₂₅,₁₅ = 2.131, the result is

Correct Answer: D [t = 1.6; do not reject H₀]

Explanation:

t = (52 − 50)/(5/4) = 1.6 < 2.131 → do not reject H₀.

76.

A fictional company claims that half of its customers are women. In a sample of 100 customers, 60 are women. The z statistic for the claim is

Correct Answer: A [2]

Explanation:

z = (0.6 − 0.5)/√(0.5 × 0.5/100) = 0.1/0.05 = 2.

77.

An estimator Tₙ is called consistent if

Correct Answer: C [Tₙ comes arbitrarily close to θ in probability as n increases]

Explanation:

Consistency is a large-sample property: P(|Tₙ − θ| < ε) → 1.

78.

Of 50 fictional workers on a night shift, 30 report poor sleep; of 50 on a day shift, 20 do. The χ² statistic (without Yates' correction) for independence of shift and sleep quality is

Correct Answer: D [4]

Explanation:

Expected 25 in each cell; χ² = 4 × 5²/25 = 4.

79.

In a fictional random sample of 150 farmers, 60 use drip irrigation. Taking z = 1.96, an approximate 95% confidence interval for the proportion is

Correct Answer: B [0.3216 to 0.4784]

Explanation:

p̂ = 0.4; SE = √(0.4 × 0.6/150) = 0.04; 0.4 ± 1.96 × 0.04.

80.

For H₀: μ = 500 against H₁: μ < 500, the test is

Correct Answer: A [left-tailed (one-tailed)]

Explanation:

The rejection region lies only in the left tail because H₁ says μ < 500.

81.

Two large fictional samples of 50 each give means 68 and 65, with σ₁ = 6 and σ₂ = 8. The z statistic for the difference of means is about

Correct Answer: D [2.12]

Explanation:

SE = √(36/50 + 64/50) = √2 ≈ 1.414; z = 3/1.414 ≈ 2.12.

82.

Five fictional meter readings are 3, 5, 9, 11, 12. Dividing by n − 1, the estimate of the population variance is

Correct Answer: B [15]

Explanation:

Mean 8; Σ(x − 8)² = 60; s² = 60/(n − 1) = 60/4 = 15.

83.

A test gives p-value 0.03. At the 5% level of significance, the decision is

Correct Answer: A [reject H₀, because the p-value is below 0.05]

Explanation:

Reject H₀ whenever p-value ≤ α; 0.03 < 0.05 (but it would not be rejected at 1%).

84.

Scores of three fictional groups: A – 5, 7, 9; B – 8, 10, 12; C – 11, 13, 15. The one-way ANOVA F ratio is

Correct Answer: C [6.75]

Explanation:

Means 7, 10, 13; SSB = 3(9 + 0 + 9) = 54; SSW = 3 × 8 = 24; F = (54/2)/(24/6) = 6.75.

85.

A fictional one-way ANOVA compares 5 brands with 25 observations in all; SST = 200 and SSB = 80. The F statistic is

Correct Answer: C [3.33]

Explanation:

SSE = 120; MSB = 80/4 = 20; MSE = 120/20 = 6; F = 20/6 ≈ 3.33.

86.

In a fictional experiment with 25 observations, the grand total of all observations is 150. The correction factor G²/N used in ANOVA is

Correct Answer: B [900]

Explanation:

CF = 150²/25 = 22500/25 = 900.

87.

In one-way ANOVA, the mean square within groups (MSE) is an unbiased estimate of

Correct Answer: A [the common error variance σ², whether or not H₀ is true]

Explanation:

MSE uses only within-group variation; MSB estimates σ² only when the means are equal.

88.

Statement-basedConsider the statements:
I. The F ratio in ANOVA can never be negative.
II. If all the sample group means are equal, the between-groups sum of squares is zero.
Which statement(s) is/are correct?

Correct Answer: C [Both I and II]

Explanation:

F = MSB/MSE, a ratio of mean squares (sums of squares divided by their df), so F ≥ 0; SSB = Σnᵢ(x̄ᵢ − x̄)² = 0 when all x̄ᵢ = x̄.

89.

Fictional yearly production for 2019–2023 is 8, 11, 13, 16, 22. Fitting y = a + bx by least squares with x = −2, −1, 0, 1, 2, the value of b is

Correct Answer: D [3.3]

Explanation:

Σxy = 33, Σx² = 10 → b = 3.3; a = ȳ = 14.

90.

The seasonal indices of a fictional product for quarters 1, 2 and 3 are 112, 96, 84. The index for quarter 4 is

Correct Answer: B [108]

Explanation:

Quarterly indices total 400: 400 − 292 = 108.

91.

A fictional store sold ₹ 450 thousand of woollens in a quarter whose seasonal index is 125. The deseasonalised (seasonally adjusted) sales are

Correct Answer: D [₹ 360 thousand]

Explanation:

Y/S × 100 = 450/125 × 100 = 360.

92.

Sudden, unforeseen changes in a time series caused by floods, strikes or wars are called

Correct Answer: A [irregular variations]

Explanation:

Erratic, unpredictable movements due to chance events are irregular (random) variations.

93.

Quarterly sales of a fictional shop: 8, 12, 10, 14, 16, 12. The first centred 4-quarterly moving average (placed against the third quarter) is

Correct Answer: C [12]

Explanation:

4-quarter averages 11, 13; centred = (11 + 13)/2 = 12.

94.

A sharp fall in a fictional factory's output in one month because of a flood is an example of

Correct Answer: C [irregular (random) variation]

Explanation:

Sudden, unpredictable one-off events cause irregular variation.

95.

Fictional data for a canteen:
Tea (kg): base price ₹ 200, base quantity 2, current price ₹ 250, current quantity 2
Milk (litre): base price ₹ 40, base quantity 30, current price ₹ 50, current quantity 25
Bread (packet): base price ₹ 30, base quantity 10, current price ₹ 36, current quantity 12
Paasche's price index is

Correct Answer: A [123.98]

Explanation:

Σp₁q₁ = 2182, Σp₀q₁ = 1760; index ≈ 123.98.

96.

Prices of three fictional items rose from ₹ 20, 50, 10 to ₹ 25, 60, 14. The index by the simple arithmetic mean of price relatives is

Correct Answer: D [128.33]

Explanation:

Relatives 125, 120, 140; mean = 128.33.

97.

For a fictional basket, Laspeyres' index is 121 and Paasche's index is 100. Fisher's index is

Correct Answer: B [110]

Explanation:

Answer: 110. √(121 × 100) = √12100 = 110.

98.

An index number formula satisfies the time reversal test if (P₀₁ = index for year 1 on base 0)

Correct Answer: D [P₀₁ × P₁₀ = 1]

Explanation:

Reversing the two periods must give the reciprocal index; Fisher's index passes this test.

99.

In a fictional town the consumer price index now stands at 160 (base = 100). What is one rupee now worth in base-year rupees?

Correct Answer: C [₹ 0.625]

Explanation:

100/160 = 0.625, i.e. 62.5 paise.

100.

A fictional family's budget weights are food 40, housing 25, clothing 15, others 20, and the group price relatives are 150, 120, 110, 130. By the family budget method, the cost of living index is

Correct Answer: B [132.5]

Explanation:

Σw R/Σw = (6000 + 3000 + 1650 + 2600)/100 = 132.5.

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