Statistics & Math interview questions

Showing 31–60 of 439 results

• Explain Training R-Squared After Adding a Random FeatureMedium

  Prove that ordinary training R-squared cannot decrease when adding a feature, while adjusted and test-set R-squared can.

  C3 AIData ScientistStatistics & MathOnline Assessment
• Explain the Gaussian Distribution and Its LimitsMedium

  Tests a candidate's mathematical understanding of the Gaussian distribution, key theoretical properties such as affine closure and the Central Limit Theorem, and the ability to diagnose and handle non-normal distributions in real-world modeling.

  C3 AIData ScientistStatistics & MathTechnical Screen
• Compute A/B significance, CI, and powerMedium

  This question evaluates proficiency in statistical inference for A/B testing—specifically two-proportion z-tests, construction of confidence intervals with unpooled standard errors, sample-size and power calculations, and multiple-comparison correction via Bonferroni.

  CVS HealthData ScientistStatistics & MathOnline Assessment
• Explain p-value and choose correct testMedium

  This question evaluates a candidate's understanding of statistical inference, hypothesis testing, and robust test selection, focusing on p-value interpretation and choosing between paired vs independent and parametric vs rank-based tests.

  CVS HealthData ScientistStatistics & MathTechnical Screen
• Calculate Annual Profit of Credit Card PortfolioEasy

  Evaluates annual profit calculation for a credit-card portfolio with monthly and annual revenue and cost components. Strong answers annualize figures, compute per-card profit, and scale to portfolio profit.

  Capital OneData ScientistStatistics & MathHR Screen
• Calculate Incremental Customers for Marketing Spend JustificationEasy

  Evaluates incremental customer calculations for partnership marketing spend justification. Strong answers derive break-even customers for fixed spend and required volume for variable-cost campaigns against a profit target.

  Capital OneData ScientistStatistics & MathHR Screen
• Calculate break-even new customers for a 30% Rent-a-Home discountMedium

  A Capital One data-scientist technical screen on break-even and unit economics for a 30%-off Rent-a-Home promotion. You set up and solve the break-even equation for incremental new customers, size it against the 2M cardholder base, then re-solve under spend-uplift assumptions and explain why the required count nearly doubles.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Calculate first-year profit marginEasy

  This question evaluates a data scientist's quantitative reasoning about unit economics and financial metrics, including understanding fixed versus variable costs and computing profit margin as a percentage.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Calculate profit and break-even across pricing modelsEasy

  This question evaluates understanding of unit economics, break-even analysis, and pricing-model effects on profitability by requiring computation of revenue, variable and fixed costs, and profit under per-GB and two-tier pricing scenarios.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compare average profit across mix scenariosEasy

  This question evaluates understanding of expected value, weighted averages, and profit-margin analysis within the Statistics & Math domain for a Data Scientist role. It is commonly asked to probe quantitative reasoning about pricing and cost trade-offs, and it tests practical application of arithmetic and scenario-based profit modeling rather than abstract theoretical concepts.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compare average unit profit under mix shiftEasy

  This question tests the candidate's ability to calculate weighted averages and understand how changes in sales volume distribution (mix shift) affect the overall average profit per unit.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute Groupon unit economics and break-evenEasy

  A Capital One data science technical screen case on restaurant unit economics with a Groupon-style voucher. You compute baseline daily profit from a 20-table day, derive the break-even check for a voucher table under a $30-for-$15 offer with a 40% commission, profit a mixed 25-table day, and decompose the profit change into traffic, check size and voucher cost. Full worked arithmetic, a sensitivity solve, and the incrementality follow-ups an interviewer expects.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute Optimal Die Re-roll StrategyEasy

  This question tests the ability to calculate expected values and determine optimal decision thresholds in a multi-stage probabilistic game.

  Capital OneData ScientistStatistics & MathOnsite
• Compute and interpret 95% confidence intervalsMedium

  This question evaluates proficiency with confidence intervals, hypothesis testing for proportions and means, multiple-comparison adjustment (Bonferroni), and sample size calculations, including assessment of normal-approximation versus Wilson score methods.

  Capital OneData ScientistStatistics & MathOnline Assessment
• Compute credit-card portfolio profit and breakevenMedium

  This question evaluates financial modeling, unit-economics calculation, breakeven analysis, and basic risk/expected-loss estimation relevant to a Data Scientist, testing competency in statistics & math and algebraic derivation within financial analysis.

  Capital OneData ScientistStatistics & MathOnsite
• Compute current annual profitEasy

  This question evaluates numerical proficiency in financial arithmetic, unit-aware quantitative reasoning, and per-customer business-metric computation within a loyalty program context.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute expansion profits and expected valueMedium

  This question evaluates financial modeling, expected-value decision-making, probability reasoning, and sensitivity analysis skills applied to revenue, variable and fixed cost interactions and contractual fee impacts, aimed at a Data Scientist role.

  Capital OneData ScientistStatistics & MathOnsite
• Compute incremental profit, breakeven, and revenue sensitivityEasy

  A Capital One data scientist technical-screen case on cost accounting and profitability modeling. Candidates compute the Year-1 incremental profit of a new vegan burger line, decompose it into fixed versus variable components, derive breakeven volume, and run a ±10% sensitivity analysis.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute optimal stopping in a die-rolling gameMedium

  This question evaluates a candidate's grasp of optimal stopping theory, expected value computation, and finite-horizon decision-making under uncertainty, including recognition of threshold-based policies and backward-induction reasoning relevant to data scientist roles.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute profit and break-even for membershipsMedium

  This problem tests your ability to model unit economics for a subscription-based loyalty program and perform sensitivity analysis to determine the break-even point for a business intervention.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute required output to recover 10% investmentMedium

  This question evaluates a candidate's ability to perform cost-volume-profit analysis and quantitative financial modeling, assessing skills in algebraic formulation of profit equations, capacity constraint evaluation, and derivation of generalized feasibility formulas.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Compute unit economics and insurance break-evenMedium

  This question evaluates a candidate's proficiency in unit economics, insurance break-even analysis, expected-value modeling, churn effects, pricing versus demand trade-offs, and basic statistical inference including MLE and confidence intervals.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Determine Claim Rate for Breakeven in Insurance PortfolioMedium

  Evaluates weather-insurance portfolio profitability from premiums, servicing, regulatory costs, and expected claims. Strong answers derive break-even claim rate, segment-selection rules, and incremental profit formulas.

  Capital OneData ScientistStatistics & MathOnsite
• Determine Factors Influencing Airline Flight Delays StatisticallyMedium

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Determine Factors Influencing Airline Flight Delays Statistically states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Determine intersection dimension of two 4D subspacesMedium

  This question tests the application of the Grassmann Dimension Formula to determine the possible dimensions of the intersection of two subspaces within a larger vector space.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Diagnose and fix a flight-delay modeling setupHard

  This question evaluates proficiency in statistical modeling for binary outcomes, including concepts such as appropriate model choice and link functions, categorical encoding, ETL-driven data quality issues, multicollinearity diagnostics (e.g.

  Capital OneData ScientistStatistics & MathOnsite
• Differentiate fixed and variable costs with examplesEasy

  This question evaluates understanding of cost classification and unit economics—specifically the distinction between fixed and variable costs—and the competency to apply those concepts within a subscription streaming business context.

  Capital OneData ScientistStatistics & MathHR Screen
• Estimate Default Rates Using Logistic Regression ModelMedium

  This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Estimate Default Rates Using Logistic Regression Model states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

  Capital OneData ScientistStatistics & MathOnsite
• Evaluate ROI and payback for renewablesMedium

  This question evaluates competency in financial modeling and quantitative analysis for utility-scale renewable projects, testing skills in ROI and payback calculation, unit economics, capacity constraint analysis, sensitivity analysis, and scenario comparison.

  Capital OneData ScientistStatistics & MathTechnical Screen
• Evaluate payback and sensitivity for solar vs ethanol pilotsMedium

  This question evaluates quantitative financial modeling and sensitivity analysis skills—specifically expected-value computation, simple payback estimation, and scenario-based risk quantification for renewable-energy pilots.

  Capital OneData ScientistStatistics & MathTechnical Screen