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Statistics Past Paper MCQs
Statistics 2024 MCQs
1 / 20
F-distribution curve in respect of tails is:
The F-distribution is right-skewed (positive skew), with a longer tail on the right.
2 / 20
The headings of the rows given in the first column of a table are called:
Stubs are row headings (e.g., "Age Group").
Captions (B) are column headings (e.g., "Frequency").
3 / 20
A study based on complete enumeration is known as:
A census survey involves collecting data from every member of a population.
A sample survey (A) studies a subset, while a pilot survey (B) is a small preliminary study.
4 / 20
Let X has a random variable U(0,1), then the variable y = -2 log X follows:
If X ~ Uniform(0,1), *Y = –2 ln(X)* follows a chi-square distribution with 2 df (a special case of exponential/Gamma).
5 / 20
With the help of ogive curve, one can determine:
An ogive (cumulative frequency curve) can find median (50th percentile), deciles (10th, 20th, etc.), and percentiles.
6 / 20
The individual probabilities of occurrence of two events A and B are known, the probability of occurrence of both the events together will be:
Without knowing if A and B are independent, we cannot determine P(A∩B). The question lacks sufficient info, but (D) is the safest default.
7 / 20
Extreme values have no effect on:
The median is the middle value and is resistant to outliers, unlike the mean (A), which is sensitive to extremes.
8 / 20
A random sample of 17 items from a heap of machine parts gives a mean of 42 and S.D.= 6.25. The value of statistic t to test the hypothesis that the population mean = 38 is:
t = (Sample Mean – Hypothesized Mean) / (S.D./√n) = (42–38)/(6.25/√17) ≈ 4/1.516 ≈ 2.64.
9 / 20
Statistical results are:
Statistics deals with general trends and probabilities, not absolute truths (A) or universal truths (D).
10 / 20
In case of weighted mean, the accuracy or utility of the mean:
Weighted mean accounts for varying importance of data points, improving accuracy over a simple average.
11 / 20
If the estimated value of an item is 50 and its actual value is 60, the relative error is:
Relative Error = (|Actual – Estimated|) / Actual = (|60 – 50|)/60 = 10/60 ≈ 0.166 (rounded to 0.16).
12 / 20
The shape of Chi-square distribution curve with 1 or 2 degrees of freedom is:
For df=1 or 2, the chi-square distribution is highly right-skewed, resembling a "J". It becomes bell-shaped (D) for higher df.
13 / 20
If all observations in a set of observations are the same, the variance of the set of values is:
Variance measures spread. If all values are identical, there is no spread → variance = 0.
14 / 20
The value 43,572.6 approximated to the thousandth place by adding figure is:
The thousandth place is the third digit from the left (3 in 43,572.6).
The next digit (5) is ≥5, so we round up: 43,572.6 → 44,000.
15 / 20
If a constant value is subtracted from each observation of a set, the mean of the set is:
The mean shifts by the same constant. If you subtract *k*, the new mean = old mean – *k*. The relative values remain unchanged.
16 / 20
The distribution for which the moment generating function does not exist but moments exist is:
Pareto distribution (heavy-tailed) has no MGF for some parameters, but moments (mean, variance) may exist.
17 / 20
For a Bernoulli distribution with probability p of a success and q of a failure, the relation between mean and variance that holds is:
Mean (μ) = *p*; Variance (σ²) = pq = p(1–p).
For *p* < 0.5, *p* < p(1–p) → Mean < Variance.
18 / 20
If a discrete random variable takes on four values -1, 0, 3, 4 with probabilities 1/6, k, 1441 and 1 - 6k, where k is a constant, then the value of k is:
Sum of probabilities = 1: 16+k+14+(1−6k)=161+k+41+(1−6k)=1 → Solve for *k*: 512−5k=0125−5k=0 → *k* = 5/24.
19 / 20
In a grouped data, the number of classes preferred are:
Too few classes (A) lose detail; too many (C) overcomplicate. An adequate number balances clarity and precision.
20 / 20
If a random variable X has mean 3 and S.D.= 5, then the variance of the variable Y = 2X - 5 is:
Variance of Y = a² × Var(X), where *a* is the coefficient of X (here, *a*=2).
Var(X) = S.D.² = 25 → Var(Y) = 4 × 25 = 100.
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