300+ Statistics and Probability Interview Questions

300+ Statistics and Probability Interview Questions free download

Master Probability & Statistics MCQs for Data Science & Analyst Interviews with Real-World Practice and Deep Explanation

In today’s data-driven world, understanding statistics and probability is a core requirement for every data science and analytics role. This course is designed specifically to prepare students and professionals for real-world data interviews through a targeted multiple-choice format that tests both foundational and advanced concepts.

Topics are :-

Statistics & Probability (Deep Dive)

I. Statistics

A. Descriptive Statistics (Difficulty: Easy to Medium) - ~50 MCQs

Measures of Central Tendency (15 MCQs)

• Topics: Mean, Median, Mode, Weighted Mean, Trimmed Mean

• Subtopics: Calculation, properties, sensitivity to outliers, when to use each

Measures of Dispersion (Variability) (15 MCQs)

• Topics: Range, Interquartile Range (IQR), Variance, Standard Deviation, Mean Absolute Deviation (MAD)

• Subtopics: Calculation, interpretation, population vs. sample variance/standard deviation (Bessel's correction)

Shape of Distribution (10 MCQs)

• Topics: Skewness (positive, negative, zero), Kurtosis (leptokurtic, mesokurtic, platykurtic)

• Subtopics: Interpretation, visual representation (histograms, box plots), impact on data analysis

Data Types & Levels of Measurement (5 MCQs)

• Topics: Nominal, Ordinal, Interval, Ratio

• Subtopics: Characteristics and appropriate statistical analyses for each

Outliers (5 MCQs)

• Topics: Definition, identification (IQR method, Z-score), impact on statistical measures, handling strategies

• Subtopics: Robust statistics, winsorization

B. Inferential Statistics (Difficulty: Medium to Hard) - ~100 MCQs

Sampling and Sampling Distributions (15 MCQs)

• Topics: Population vs. Sample, Sampling techniques (Simple Random, Stratified, Systematic, Cluster, Convenience, Quota)

• Subtopics: Sampling error, bias (selection bias, sampling bias)

Central Limit Theorem (CLT) (10 MCQs)

• Topics: Statement, assumptions, importance in hypothesis testing and confidence intervals

• Subtopics: Sample mean distribution

Estimation (15 MCQs)

• Topics: Point Estimates, Interval Estimates (Confidence Intervals)

• Subtopics: Interpretation of confidence intervals (e.g., 95% CI), margin of error, factors affecting confidence interval width

Hypothesis Testing (25 MCQs)

• Topics: Null Hypothesis (H₀), Alternative Hypothesis (H₁)

• Subtopics: Type I Error (α, false positive), Type II Error (β, false negative), Power of a test (1−β)

• P-value: Definition, interpretation, significance level

Common Statistical Tests (25 MCQs)

• Topics: Z-test, T-test (one-sample, two-sample independent/dependent), ANOVA (One-way, Two-way), Chi-Square Test (Goodness of Fit, Independence)

• Subtopics: Assumptions of each test, when to use which test, interpretation of test statistics

Regression Analysis (10 MCQs)

• Topics: Simple Linear Regression, Multiple Linear Regression

• Subtopics: Assumptions (linearity, independence, homoscedasticity, normality of residuals), interpretation of coefficients, R-squared, Adjusted R-squared, Residual analysis

C. Advanced Statistical Concepts (Difficulty: Hard) - ~90 MCQs

ANOVA (Analysis of Variance) (10 MCQs)

• Topics: F-statistic, degrees of freedom, post-hoc tests (Tukey HSD)

• Subtopics: Understanding variance decomposition

Non-parametric Tests (10 MCQs)

• Topics: Mann-Whitney U test, Wilcoxon Signed-Rank test, Kruskal-Wallis test

• Subtopics: When to use non-parametric vs. parametric tests

Correlation and Causation (15 MCQs)

• Topics: Pearson correlation coefficient, Spearman's rank correlation

• Subtopics: Difference between correlation and causation, spurious correlations

Multicollinearity (10 MCQs)

• Topics: Definition, detection, consequences, handling techniques (VIF, regularization)

Regularization (Lasso, Ridge, Elastic Net) (10 MCQs)

• Topics: Purpose (bias-variance trade-off, feature selection), L1 vs. L2 penalties

• Subtopics: How they work in regression models

A/B Testing (Experimental Design) (20 MCQs)

• Topics: Design of experiments, control group, treatment group, hypothesis formulation for A/B tests, power analysis for sample size

• Subtopics: Metrics, common pitfalls (e.g., novelty effect, selection bias in experiments)

Maximum Likelihood Estimation (MLE) (15 MCQs)

• Topics: Concept, applications in model parameter estimation

• Subtopics: Basic understanding of likelihood function

II. Probability

A. Basic Probability (Difficulty: Easy to Medium) - ~20 MCQs

Fundamentals (5 MCQs)

• Topics: Sample space, Events, Outcomes, Axioms of Probability

• Subtopics: Union, Intersection, Complement of events

Types of Probability (5 MCQs)

• Topics: Classical, Empirical, Subjective

Conditional Probability (5 MCQs)

• Topics: Definition, P(A∣B), independent events

• Subtopics: Multiplication Rule for independent/dependent events

Permutations and Combinations (5 MCQs)

• Topics: Factorials, permutations (with/without repetition), combinations (with/without repetition)

• Subtopics: When to use each in counting problems

B. Probability Distributions (Difficulty: Medium to Hard) - ~40 MCQs

Discrete Probability Distributions (15 MCQs)

• Topics: Bernoulli, Binomial, Poisson, Uniform (Discrete)

• Subtopics: Probability Mass Function (PMF), Expected Value (E[X]), Variance (Var[X]), identifying real-world scenarios for each

Continuous Probability Distributions (15 MCQs)

• Topics: Normal (Gaussian), Exponential, Uniform (Continuous), Log-Normal

• Subtopics: Probability Density Function (PDF), Cumulative Distribution Function (CDF), Expected Value, Variance, identifying real-world scenarios for each

Joint and Marginal Distributions (5 MCQs)

• Topics: Joint PMF/PDF, Marginal PMF/PDF

• Subtopics: Understanding relationships between multiple random variables

Bayes' Theorem (5 MCQs)

• Topics: Statement of Bayes' Theorem

• Subtopics: Prior probability, Likelihood, Posterior probability, application in Bayesian inference

Much More !!!