Statistics & Math Interview Questions

Showing 61–90 of 218 results

• DatabricksEasy·Data Scientist
  Relate coefficients under linear feature transformation

  This question tests the relationship between regression coefficients when predictors undergo linear transformations, specifically focusing on scaling and centering transformations.

  Statistics & MathTechnical ScreenLinear RegressionLinear AlgebraFeature Engineering
• DatabricksHard·Data Scientist
  Test coin fairness from 560 tails in 1000 flips

  This problem evaluates hypothesis testing for proportions—formulating null and alternative hypotheses, applying the binomial-to-normal approximation, and interpreting p-values; it belongs to Statistics & Math for Data Scientist roles and is pitched at an introductory/undergraduate applied statistics level.

  Statistics & MathTechnical Screen
• DDeshawHard·Software Engineer
  Compare Fixed and Variable Train Gaps Without a Timetable

  Compare two train services for a commuter who arrives without consulting a timetable. Explain the assumptions and derivation clearly, check edge cases, and show how the result changes when those assumptions no longer hold.

  Statistics & MathTechnical Screen
• DoorDashMedium·Data Scientist
  Calculate power and test duration

  This question evaluates proficiency in statistical power analysis, sample size calculation for proportions, hypothesis testing for two-sided z-tests, and practical experiment duration estimation for A/B testing.

  Statistics & MathTechnical Screen
• DoorDashMedium·Data Scientist
  Compute sample sizes and error control

  This question evaluates proficiency in experimental design and applied inferential statistics—specifically sample size calculation for means and proportions, non-inferiority testing, multiple-comparison error control, cluster-randomized design effects, and sequential monitoring boundaries—within the Statistics & Math domain for a Data Scientist role. It is commonly asked to measure the ability to apply statistical formulas and error-control principles under practical constraints, balancing power and type I error while accounting for clustering and interim looks; the assessment emphasizes practical application grounded in conceptual understanding of inferential methods.

  Statistics & MathTechnical Screen
• DoorDashHard·Data Scientist
  Design A/B Test to Evaluate Algorithm's Revenue Impact

  DoorDash statistics and experimentation prompt on A/B testing a recommendation algorithm's revenue impact, covering hypotheses, randomization, sample size, heavy-tailed revenue, p=0.08 interpretation, and causal alternatives.

  Statistics & MathTechnical Screen
• EExaHard·Machine Learning Engineer
  Design a Streaming Percentile Estimator

  Design a streaming percentile estimator without storing every observation, and define rank error precisely. Compare a deterministic single-stream summary with t-digest-style centroids across memory, update cost, duplicates, skew, tail accuracy, and distributed merge limitations.

  Statistics & MathTechnical Screen
• ExperianEasy·Data Scientist
  Calculate Expected Flips for Two Heads Coin Toss

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Calculate Expected Flips for Two Heads Coin Toss states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• Goldman SachsMedium·Quantitative Researcher
  Estimate Pi with a Square Cardboard and a Fair Die to 5-6 Decimal Places

  Using only a square piece of cardboard and a fair six-sided die, design an experiment that estimates pi empirically, then explain how many trials 5 to 6 correct decimal places would require and how you would get there. It tests Monte Carlo design, bias versus variance, and error analysis.

  Statistics & MathTechnical Screen
• Goldman SachsMedium·Quantitative Researcher
  From Alpha Signal to Portfolio: Reliability, Regime Dependence and Entropy

  Walk through how a quantitative equity team turns a predictive signal into portfolio holdings, then explain how to judge whether the signal is reliable, whether its performance depends on the market regime, and how entropy and mutual information can be used to evaluate signals and portfolios.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Analyze Linear Regression Changes with Duplicated Observations

  Evaluates regression and hypothesis-testing interpretation under duplicated observations and large samples. Strong answers show unchanged OLS coefficients, standard-error effects, p-value meaning, and practical chi-square adjustments.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Analyze data duplication effects in linear regression

  This question evaluates understanding of OLS estimation, the effects of duplicated observations on estimator variance and inference, and the interplay between sample size, p-values, and effect-size measures within the Statistics & Math domain for a Data Scientist role.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Approximate a percentile from buckets

  This question tests the ability to interpolate values within histogram buckets to estimate a specific percentile, requiring an understanding of linear versus log-space assumptions.

  Statistics & MathTechnical ScreenStatisticsEstimationAlgorithms
• GoogleMedium·Data Scientist
  Assess Fundamental Statistics Knowledge in Data-Science Interviews

  Google data scientist statistics prompt covering MLEs for normal mean and variance, conditional density from a joint pdf, standard normal pdf and cdf, and assumptions for unbiased estimators.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Derive MLEs and conditional Normal distributions

  This question evaluates proficiency in parametric inference and probability theory, specifically maximum likelihood estimation, bias of estimators, and conditioning in univariate and bivariate Normal distributions including constrained estimation of parameters.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Determine Impact of New Chat-Notification on User Engagement

  Determine Impact of New Chat-Notification on User Engagement evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Statistics & MathTechnical Screen
• GoogleEasy·Data Scientist
  Determine Normality of Single Observation with Z-Test

  Evaluates hypothesis testing for a single observation against a fully specified standard normal distribution. Strong answers state hypotheses, use z = x, define critical values and p-values, and note limitations.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Estimate percentile from buckets

  Estimate a percentile from histogram buckets by locating the cumulative-count bucket, explaining why midpoint can be poor, interpolating within the bucket under explicit assumptions, handling log-spaced buckets and edge cases, and reporting uncertainty when buckets are coarse.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Estimate population singletons from a 10% log

  This question evaluates mastery of statistical estimation and sampling theory, including recognition of bias from subsampling, frequency‑of‑frequencies modeling for rare events, uncertainty quantification under heavy‑tailed counts, and design of simulation studies.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Estimate unbiased ad scores with many reviewers

  This problem tests the ability to design an estimation framework that accounts for rater bias and variance, specifically applying concepts like hierarchical modeling or fixed-effect normalization to estimate latent variables.

  Statistics & MathTechnical ScreenStatisticsModelingBias
• GoogleHard·Data Scientist
  Explain Bootstrap and Prove Uniformity

  This question tests the conceptual understanding of bootstrap resampling for variance estimation and the mathematical proof of probability distributions using the properties of the Uniform distribution.

  Statistics & MathTechnical ScreenStatisticsProbabilityBootstrap
• GoogleHard·Data Scientist
  Explain Bootstrap and Statistical Inference

  This problem tests your understanding of bootstrap resampling theory, confidence interval construction, and the statistical trade-offs involved in hypothesis testing for small-sample experiments.

  Statistics & MathTechnical ScreenBootstrapHypothesis TestingMLE
• GoogleMedium·Data Scientist
  Explain Simpson’s Paradox and Its Causes with Example

  Evaluates Simpson's paradox through definition, confounding, subgroup imbalance, and a numeric reversal example. Strong answers compare stratified and aggregate rates and explain when each comparison matters.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Explain and resolve Simpson’s paradox

  This question evaluates understanding of Simpson's paradox, confounding, and causal reasoning, checking numerical interpretation of subgroup versus aggregate statistics and the ability to recognize when aggregated averages can mislead.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Generate Samples from Truncated Normal Distribution

  Evaluates truncated normal distribution fundamentals and sampling methods for lower-tail truncation. Strong answers name the lower-truncated normal, provide the PDF and CDF, and compare inverse-CDF, rejection, and tail-efficient samplers.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Generate Uniform Samples and Estimate Percentiles

  This problem tests the ability to generate uniform spatial samples using standard random functions and the mathematical application of linear interpolation for percentile estimation from binned data.

  Statistics & MathTechnical ScreenProbabilityStatisticsInterpolation
• GoogleMedium·Data Scientist
  Infer distribution and choose robust statistics

  This problem tests the ability to diagnose non-normal data distributions (specifically zero-inflated, heavy-tailed data) and select appropriate statistical metrics for hypothesis testing.

  Statistics & MathTechnical ScreenStatisticsData DistributionsHypothesis Testing
• GoogleMedium·Data Scientist
  Measure Bird Species Segregation

  This question evaluates spatial statistical reasoning, ecological data analysis, and the ability to formulate hypotheses, choose appropriate segregation metrics, and account for confounders and sampling bias.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Narrow a confidence interval for a mean

  This question evaluates understanding of confidence intervals, the relationship between sample size and interval width, variance-reduction techniques, the impact of changing confidence levels, and the ability to communicate statistical risk and design-based trade-offs.

  Statistics & MathTechnical Screen
• GoogleMedium·Data Scientist
  Prove OLS invariance to linear transforms

  This question evaluates understanding of linear regression invariance under invertible linear transformations, multivariate linear algebra, and the impact of regularization (ridge and lasso) on coefficient and prediction stability in the Statistics & Math domain.

  Statistics & MathTechnical Screen