Statistics & Math Interview Questions

Showing 31–60 of 439 results

• C3 AIMedium·Data Scientist
  Explain Training R-Squared After Adding a Random Feature

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

  Statistics & MathOnline Assessment
• C3 AIMedium·Data Scientist
  Explain the Gaussian Distribution and Its Limits

  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.

  Statistics & MathTechnical ScreenStatisticsProbabilityAnomaly Detection
• CVS HealthMedium·Data Scientist
  Compute A/B significance, CI, and power

  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.

  Statistics & MathOnline Assessment
• CVS HealthMedium·Data Scientist
  Explain p-value and choose correct test

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Calculate Annual Profit of Credit Card Portfolio

  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.

  Statistics & MathHR Screen
• Capital OneEasy·Data Scientist
  Calculate Incremental Customers for Marketing Spend Justification

  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.

  Statistics & MathHR Screen
• Capital OneMedium·Data Scientist
  Calculate break-even new customers for a 30% Rent-a-Home discount

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Calculate first-year profit margin

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Calculate profit and break-even across pricing models

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Compare average profit across mix scenarios

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Compare average unit profit under mix shift

  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.

  Statistics & MathTechnical ScreenStatisticsWeighted AverageUnit Economics
• Capital OneEasy·Data Scientist
  Compute Groupon unit economics and break-even

  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.

  Statistics & MathTechnical Screen
• Capital OneEasy·Data Scientist
  Compute Optimal Die Re-roll Strategy

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

  Statistics & MathOnsiteProbabilityExpected ValueDecision Theory
• Capital OneMedium·Data Scientist
  Compute and interpret 95% confidence intervals

  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.

  Statistics & MathOnline Assessment
• Capital OneMedium·Data Scientist
  Compute credit-card portfolio profit and breakeven

  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.

  Statistics & MathOnsite
• Capital OneEasy·Data Scientist
  Compute current annual profit

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

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Compute expansion profits and expected value

  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.

  Statistics & MathOnsite
• Capital OneEasy·Data Scientist
  Compute incremental profit, breakeven, and revenue sensitivity

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Compute optimal stopping in a die-rolling game

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Compute profit and break-even for memberships

  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.

  Statistics & MathTechnical ScreenEconomicsLinear ModelingBreak-even Analysis
• Capital OneMedium·Data Scientist
  Compute required output to recover 10% investment

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Compute unit economics and insurance break-even

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Determine Claim Rate for Breakeven in Insurance Portfolio

  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.

  Statistics & MathOnsite
• Capital OneMedium·Data Scientist
  Determine Factors Influencing Airline Flight Delays Statistically

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Determine intersection dimension of two 4D subspaces

  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.

  Statistics & MathTechnical ScreenLinear AlgebraVector SpacesSubspaces
• Capital OneHard·Data Scientist
  Diagnose and fix a flight-delay modeling setup

  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.

  Statistics & MathOnsite
• Capital OneEasy·Data Scientist
  Differentiate fixed and variable costs with examples

  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.

  Statistics & MathHR Screen
• Capital OneMedium·Data Scientist
  Estimate Default Rates Using Logistic Regression Model

  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.

  Statistics & MathOnsite
• Capital OneMedium·Data Scientist
  Evaluate ROI and payback for renewables

  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.

  Statistics & MathTechnical Screen
• Capital OneMedium·Data Scientist
  Evaluate payback and sensitivity for solar vs ethanol pilots

  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.

  Statistics & MathTechnical Screen