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Two Sigma·Data Scientist·Online Assessment (OA)·Intermediate

Intermediate
Apr 2026

Summary

Two Sigma data scientist interview with a statistics and regression problem that looked straightforward on paper but had enough moving parts to trip you up if you weren't careful about the implementation details.

Questions Asked (1)

Q1

Given a list of unsorted day-temperature pairs, compute the median temperature, sample variance, OLS regression slope and intercept, and a predicted temperature for a given query day index.

Algorithms & Data StructuresProduct Analytics & MetricsData Modeling
Author's notes

The median part is fine, just sort the temps and handle even/odd.

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Suggested Approach

Start by clarifying the input format, edge cases, and whether the day indices are numeric or categorical. Then outline the computations: sort for median, compute sample variance with Bessel's correction, and use closed-form OLS formulas for slope and intercept. Finally, plug the query day into the regression equation to predict temperature, and discuss any assumptions or limitations.

Pro tip: Mention that OLS assumes a linear relationship and that the median is robust to outliers, showing you understand when each statistic is appropriate. Also, proactively discuss how you would handle missing data or duplicate days, as real-world data is often messy.

1. Clarify requirements and edge cases

Ask about input format, data types, missing values, and whether the day indices are numeric or categorical. Confirm the definition of 'sample variance' (using n-1 denominator) and whether the regression should include an intercept.

2. Compute median temperature

Sort the temperature values and find the middle value (or average of two middle values if even count). Mention that sorting is O(n log n) and that the median is robust to outliers.

3. Compute sample variance

Calculate the mean temperature, then sum the squared deviations from the mean, and divide by (n-1) for sample variance. Explain why Bessel's correction is used.

4. Perform OLS regression

Use the closed-form formulas: slope = covariance(day, temp) / variance(day), intercept = mean(temp) - slope * mean(day). Discuss assumptions like linearity and independence.

5. Predict and validate

Plug the query day into the regression equation to predict temperature. Mention that predictions outside the range of observed days are extrapolations and should be treated with caution.

Key Points to Mention

  • Median is robust to outliers; sorting is O(n log n).
  • Sample variance uses n-1 denominator (Bessel's correction) for unbiased estimation.
  • OLS slope and intercept can be computed via closed-form formulas using means and covariances.
  • Regression assumes a linear relationship, independence, and homoscedasticity.
  • Prediction for a given day is ŷ = intercept + slope * day.
  • Handle edge cases: empty list, single data point, duplicate days, missing values.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.