100 challenging multiple-choice questions on descriptive statistics, inferential methods, and time series analysis. Inspired by real data science and analytics interview questions from FAANG, consulting firms, and quant roles.
1. Which measure of central tendency is most affected by extreme outliers?
✅ Correct Answer: c) Mean
📝 Explanation:
The mean incorporates every value and is pulled toward extreme scores.
2. In a positively skewed distribution, the correct order of mean, median, and mode is:
✅ Correct Answer: a) Mean > Median > Mode
📝 Explanation:
The tail on the right pulls the mean highest, followed by median, then mode.
3. The interquartile range (IQR) is calculated as:
✅ Correct Answer: b) Q3 – Q1
📝 Explanation:
IQR measures spread between the 75th and 25th percentiles.
4. Which of the following is NOT a measure of dispersion?
✅ Correct Answer: d) Median
📝 Explanation:
Median describes location, not spread.
5. The empirical rule applies to data that are approximately:
✅ Correct Answer: b) Normally distributed
📝 Explanation:
About 68%, 95%, and 99.7% fall within 1, 2, and 3 standard deviations.
6. Pearson's correlation coefficient is undefined when:
✅ Correct Answer: a) Variance of X or Y is zero
📝 Explanation:
Division by zero standard deviation makes r undefined.
7. Boxplot whiskers typically extend to:
✅ Correct Answer: b) 1.5 × IQR beyond Q1 and Q3
📝 Explanation:
Points outside are flagged as potential outliers.
8. The coefficient of variation (CV) is useful for comparing:
✅ Correct Answer: b) Relative variability when units or means differ
📝 Explanation:
CV = (σ / μ) × 100% standardizes dispersion.
9. Z-score of a value x is given by:
✅ Correct Answer: a) (x – μ) / σ
📝 Explanation:
Measures deviations in standard deviation units.
10. Chebyshev’s theorem guarantees at least what proportion within k standard deviations (k>1)?
✅ Correct Answer: b) 1 – 1/k²
📝 Explanation:
Applies to any distribution with finite variance.
11. The sampling distribution of the sample mean becomes approximately normal when n ≥ 30 due to:
✅ Correct Answer: b) Central Limit Theorem
📝 Explanation:
CLT justifies normality for large samples regardless of population shape.
12. A Type I error occurs when we:
✅ Correct Answer: b) Reject a true null
📝 Explanation:
False positive; probability equals α.
13. The p-value is the probability of obtaining a test statistic at least as extreme as observed, assuming:
✅ Correct Answer: b) H₀ is true
📝 Explanation:
Small p-value casts doubt on the null.
14. For a two-tailed z-test at α = 0.05, the critical values are:
✅ Correct Answer: b) ±1.96
📝 Explanation:
5% split equally in both tails.
15. The standard error of the mean is σ / √n; when σ is unknown we use:
✅ Correct Answer: b) Sample standard deviation s
📝 Explanation:
Leads to t-distribution with n–1 df.
16. Confidence interval width is proportional to:
✅ Correct Answer: a) 1 / √n
📝 Explanation:
Larger samples yield narrower intervals.
17. Power of a test = 1 – β, where β is:
✅ Correct Answer: b) Type II error rate
📝 Explanation:
Probability of failing to detect a true effect.
18. For proportions, the standard error is √[p(1–p)/n]; for confidence intervals we often use:
✅ Correct Answer: a) Sample proportion p̂
📝 Explanation:
Wald interval: p̂ ± z√[p̂(1–p̂)/n].
19. The chi-square test for independence tests whether:
✅ Correct Answer: a) Row and column variables are associated
📝 Explanation:
Compares observed vs expected frequencies.
20. ANOVA tests equality of:
✅ Correct Answer: b) Three or more population means
📝 Explanation:
F-statistic = MSB / MSW.
21. A time series is stationary if:
✅ Correct Answer: a) Mean, variance, and autocovariance are time-invariant
📝 Explanation:
Strict stationarity requires constant distribution.
22. The ACF at lag k measures:
✅ Correct Answer: a) Correlation between y_t and y_{t–k}
📝 Explanation:
Helps identify MA order.
23. In an AR(1) model y_t = φ y_{t–1} + ε_t, |φ| < 1 ensures:
✅ Correct Answer: a) Stationarity
📝 Explanation:
Root outside unit circle.
24. Differencing a series once removes:
✅ Correct Answer: a) Linear trend
📝 Explanation:
Δy_t = y_t – y_{t–1} eliminates polynomial trend of order 1.
25. The PACF of an MA(1) process cuts off after:
✅ Correct Answer: a) Lag 1
📝 Explanation:
Partial correlation beyond lag 1 is zero.
26. ADF test null hypothesis is:
✅ Correct Answer: a) Series has a unit root (non-stationary)
📝 Explanation:
Reject H0 ⇒ stationary.
27. In SARIMA(p,d,q)(P,D,Q)s, 's' denotes:
✅ Correct Answer: a) Seasonal period
📝 Explanation:
Common values: 12 (monthly), 4 (quarterly).
28. AIC penalizes models for:
✅ Correct Answer: a) Number of parameters
📝 Explanation:
Lower AIC indicates better balance of fit and complexity.
29. White noise has ACF values approximately:
✅ Correct Answer: a) Zero for all lags > 0
📝 Explanation:
Uncorrelated errors.
30. Holt-Winters additive model is suitable when seasonal fluctuations:
✅ Correct Answer: a) Are roughly constant in size
📝 Explanation:
Multiplicative version for proportional seasonality.
31. The variance of a dataset {2, 4, 6, 8, 10} is:
✅ Correct Answer: b) 8
📝 Explanation:
Mean = 6; variance = [(−4)² + (−2)² + 0 + 2² + 4²]/4 = 40/5 = 8.
32. For the data {1, 3, 3, 6}, the mode is:
✅ Correct Answer: b) 3
📝 Explanation:
3 appears twice; others once.
33. Skewness coefficient > 0 indicates:
✅ Correct Answer: c) Right-skewed
📝 Explanation:
Longer tail on the positive side.
34. Percentile rank of the median is:
✅ Correct Answer: b) 50th
📝 Explanation:
Half the data lie below the median.
35. Geometric mean is preferred for:
✅ Correct Answer: a) Averaging rates of change
📝 Explanation:
Handles compounding/multiplicative processes.
36. Covariance of a variable with itself equals its:
✅ Correct Answer: a) Variance
📝 Explanation:
Cov(X,X) = Var(X).
37. Spearman’s rank correlation is based on:
✅ Correct Answer: b) Ranks of the data
📝 Explanation:
Non-parametric measure of monotonic relationship.
38. The 95% CI for μ when n=25, x̄=50, s=10 (t-critical ≈ 2.064) is:
✅ Correct Answer: a) 50 ± 4.13
📝 Explanation:
Margin = 2.064 × (10/√25) = 2.064 × 2 ≈ 4.13.
39. A test statistic z = 2.5, α = 0.01 two-tailed; decision is:
✅ Correct Answer: b) Fail to reject H0
📝 Explanation:
Critical |z| = 2.576 > 2.5.
40. Minimum sample size for proportion CI with margin of error E=0.03, p*=0.5, z=1.96:
✅ Correct Answer: a) 1068
📝 Explanation:
n = (1.96² × 0.5 × 0.5) / 0.03² ≈ 1067.11 → 1068.
41. For paired t-test, degrees of freedom =
✅ Correct Answer: b) n – 1
📝 Explanation:
Based on differences (n pairs).
42. F-test is used to compare:
✅ Correct Answer: a) Two variances
📝 Explanation:
H0: σ₁² = σ₂².
43. Mann-Whitney U tests difference in:
✅ Correct Answer: a) Medians of two independent samples
📝 Explanation:
Non-parametric alternative to two-sample t-test.
44. Kruskal-Wallis is the non-parametric version of:
✅ Correct Answer: a) One-way ANOVA
📝 Explanation:
Compares three or more independent groups.
45. The Durbin-Watson statistic near 2 indicates:
✅ Correct Answer: a) No autocorrelation
📝 Explanation:
Range 0–4; 2 is ideal.
46. In exponential smoothing, α close to 1 gives more weight to:
✅ Correct Answer: a) Recent observations
📝 Explanation:
Higher α reacts faster to changes.
47. An AR(2) model requires PACF significant at:
✅ Correct Answer: a) Lags 1 and 2
📝 Explanation:
PACF cuts off after p.
48. Seasonal differencing of period 12 is denoted as:
✅ Correct Answer: a) ∇₁₂ y_t
📝 Explanation:
∇₁₂ y_t = y_t – y_{t–12}.
49. Ljung-Box test checks for:
✅ Correct Answer: a) Lack of autocorrelation in residuals
📝 Explanation:
High p-value supports white noise.
50. KPSS test null hypothesis is:
✅ Correct Answer: a) Stationarity
📝 Explanation:
Complements ADF; fail to reject ⇒ stationary.
51. In ARIMA, 'I' stands for:
✅ Correct Answer: a) Integrated
📝 Explanation:
Order of differencing to achieve stationarity.
52. Forecasts from a random walk model are:
✅ Correct Answer: a) Last observed value
📝 Explanation:
y_{t+1} = y_t + ε_{t+1} ⇒ best forecast = y_t.
53. Granger causality tests whether past values of X improve prediction of:
✅ Correct Answer: a) Y beyond its own past
📝 Explanation:
Rejects non-causality if X lags are significant in Y equation.
54. Variance inflation factor (VIF) > 10 suggests:
✅ Correct Answer: a) Severe multicollinearity
📝 Explanation:
VIF_j = 1 / (1 – R_j²).
55. The coefficient of determination R² represents:
✅ Correct Answer: a) Proportion of variance explained
📝 Explanation:
SSR / SST.
56. In simple linear regression, the least squares slope b1 =
✅ Correct Answer: a) Cov(X,Y) / Var(X)
📝 Explanation:
Minimizes sum of squared residuals.
57. Residual standard error estimates:
✅ Correct Answer: a) σ, the error standard deviation
📝 Explanation:
√(SSE / (n–2)).
58. For logistic regression, the link function is:
✅ Correct Answer: a) Logit
📝 Explanation:
log(p/(1–p)) = β0 + β1x.
59. The odds ratio exp(β) = 1.5 means:
✅ Correct Answer: a) 50% increase in odds per unit increase in x
📝 Explanation:
Odds multiply by exp(β).
60. Poisson regression is suitable for:
✅ Correct Answer: a) Count data
📝 Explanation:
Mean = variance.
61. In survival analysis, Kaplan-Meier estimates:
✅ Correct Answer: a) Survival function non-parametrically
📝 Explanation:
Product-limit estimator handles censoring.
62. Cox proportional hazards assumption is violated if:
✅ Correct Answer: a) Hazard ratios change over time
📝 Explanation:
Check via time-dependent covariates or plots.
63. Bayesian inference updates beliefs using:
✅ Correct Answer: a) Prior × Likelihood → Posterior
📝 Explanation:
Bayes’ theorem: P(θ|data) ∝ P(data|θ) P(θ).
64. Conjugate prior for normal mean (known variance) is:
✅ Correct Answer: a) Normal
📝 Explanation:
Posterior remains normal.
65. MCMC methods are used to:
✅ Correct Answer: a) Sample from complex posterior distributions
📝 Explanation:
Markov Chain Monte Carlo approximates posteriors.
66. Bootstrapping estimates sampling distribution by:
✅ Correct Answer: a) Resampling with replacement from the data
📝 Explanation:
Non-parametric; empirical distribution.
67. Percentile bootstrap CI uses:
✅ Correct Answer: a) 2.5th and 97.5th percentiles of bootstrap statistics
📝 Explanation:
For 95% CI from B=1000 replicates.
68. Cross-validation is primarily used to assess:
✅ Correct Answer: a) Model generalization error
📝 Explanation:
K-fold CV estimates out-of-sample performance.
69. The bias-variance tradeoff implies that overly complex models tend to:
✅ Correct Answer: a) Overfit (high variance, low bias)
📝 Explanation:
Capture noise, not just signal.
70. Principal Component Analysis (PCA) maximizes:
✅ Correct Answer: a) Variance along projected directions
📝 Explanation:
Eigenvectors of covariance matrix.
71. The scree plot helps determine number of PCs by looking for:
✅ Correct Answer: a) Elbow in eigenvalue decline
📝 Explanation:
Retain components before sharp drop.
72. In k-means clustering, the objective is to minimize:
✅ Correct Answer: a) Within-cluster sum of squares
📝 Explanation:
Iterative assignment and centroid update.
73. Silhouette coefficient ranges from:
✅ Correct Answer: a) –1 to +1
📝 Explanation:
Higher values indicate better cluster separation.
74. A contingency table with all expected frequencies ≥ 5 is required for:
✅ Correct Answer: a) Chi-square test validity
📝 Explanation:
Approximation to chi-square distribution.
75. McNemar’s test is used for:
✅ Correct Answer: a) Paired binary data
📝 Explanation:
Tests marginal homogeneity.
76. The central limit theorem requires random samples that are:
✅ Correct Answer: a) Independent and identically distributed
📝 Explanation:
For large n, sample mean ≈ normal.
77. Degrees of freedom for two-sample t-test (unequal variances) is approximately:
✅ Correct Answer: a) Welch-Satterthwaite formula
📝 Explanation:
Conservative; avoids equal variance assumption.
78. Effect size Cohen’s d = (μ1 – μ2) / σ; d = 0.8 is considered:
✅ Correct Answer: a) Large
📝 Explanation:
Benchmarks: 0.2 small, 0.5 medium, 0.8 large.
79. Multiple R² in regression can be artificially inflated by:
✅ Correct Answer: a) Adding irrelevant predictors
📝 Explanation:
Use adjusted R² to penalize extra terms.
80. Homoscedasticity means residuals have:
✅ Correct Answer: a) Constant variance across predicted values
📝 Explanation:
Breusch-Pagan test checks this.
81. Durbin-Watson values < 1 typically indicate:
✅ Correct Answer: a) Strong positive autocorrelation
📝 Explanation:
Values near 0 = positive; near 4 = negative.
82. In time series decomposition, the remainder after trend and seasonal removal is:
✅ Correct Answer: a) Irregular (random) component
📝 Explanation:
Should resemble white noise if model is good.
83. STL decomposition stands for:
✅ Correct Answer: a) Seasonal-Trend decomposition using LOESS
📝 Explanation:
Robust, flexible for varying seasonal patterns.
84. ACF of a seasonal series with period 12 shows spikes at:
✅ Correct Answer: a) Multiples of 12
📝 Explanation:
Indicates need for seasonal AR/MA terms.
85. Box-Cox transformation is applied to stabilize:
✅ Correct Answer: a) Variance (heteroscedasticity)
📝 Explanation:
y(λ) = (y^λ – 1)/λ or log(y) for λ=0.
86. Over-differencing a stationary series introduces:
✅ Correct Answer: a) MA(1) structure with negative coefficient
📝 Explanation:
ACF shows spike at lag 1, then near zero.
87. The optimal ARIMA model often has residuals with:
✅ Correct Answer: a) No significant ACF/PACF spikes (white noise)
📝 Explanation:
Ljung-Box p > 0.05 supports adequacy.
88. In VAR models, each variable is modeled as a function of:
✅ Correct Answer: a) Its own lags and lags of all other variables
📝 Explanation:
Vector autoregression for multivariate time series.
89. Impulse response function traces effect of a shock in one variable on:
✅ Correct Answer: a) Future values of all variables
📝 Explanation:
Shows dynamic responses in VAR.
90. Cointegration means two non-stationary series have:
✅ Correct Answer: a) A stationary linear combination
📝 Explanation:
Long-run equilibrium relationship.
91. Johansen test is used to detect:
✅ Correct Answer: a) Number of cointegrating relationships
📝 Explanation:
Trace and max-eigenvalue statistics.
92. ARCH model tests for:
✅ Correct Answer: a) Time-varying volatility (heteroscedasticity)
📝 Explanation:
Variance depends on past squared errors.
93. GARCH(1,1) models volatility as:
✅ Correct Answer: a) σ²_t = α₀ + α₁ ε²_{t–1} + β₁ σ²_{t–1}
📝 Explanation:
Combines ARCH and persistence.
94. The Jarque-Bera test assesses:
✅ Correct Answer: a) Normality of residuals (skewness + kurtosis)
📝 Explanation:
JB statistic ~ χ²(2).
95. Shapiro-Wilk test null hypothesis is:
✅ Correct Answer: a) Data come from a normal distribution
📝 Explanation:
Powerful for small samples.
96. Levene’s test checks for:
✅ Correct Answer: a) Equality of variances across groups
📝 Explanation:
Robust to non-normality.
97. The Bonferroni correction adjusts α by:
✅ Correct Answer: a) Dividing by number of tests
📝 Explanation:
Controls family-wise error rate conservatively.
98. Holm’s method is a:
✅ Correct Answer: a) Step-down multiple comparison procedure
📝 Explanation:
Less conservative than Bonferroni.
99. Tukey’s HSD test is used after ANOVA to compare:
✅ Correct Answer: a) All pairwise means
📝 Explanation:
Honest Significant Difference; assumes equal variances.
100. Dunnett’s test compares:
✅ Correct Answer: a) Multiple treatments vs a single control
📝 Explanation:
Fewer comparisons, higher power.
101. The Q-Q plot assesses normality by plotting:
✅ Correct Answer: a) Sample quantiles vs theoretical normal quantiles
📝 Explanation:
Straight line indicates normality.
102. A leverage point in regression has high:
✅ Correct Answer: a) Distance from mean of X (hat diagonal)
📝 Explanation:
h_ii > 2p/n flags potential leverage.
103. Cook’s distance measures:
✅ Correct Answer: a) Influence of an observation on all fitted values
📝 Explanation:
Large values (> 4/n) indicate influential points.
104. The partial F-test in regression compares:
✅ Correct Answer: a) Nested models (reduced vs full)
📝 Explanation:
Tests significance of added predictors.
105. Ridge regression adds penalty:
✅ Correct Answer: a) λ Σ β_j² (L2)
📝 Explanation:
Shrinks coefficients, handles multicollinearity.
106. Lasso can perform variable selection because it:
✅ Correct Answer: a) Sets some coefficients exactly to zero
📝 Explanation:
L1 penalty promotes sparsity.
107. Elastic Net combines:
✅ Correct Answer: a) Ridge and Lasso penalties
📝 Explanation:
Useful when p > n or high correlation.
