I jumped straight into the sample variance formula without asking which type they wanted, and the interviewer had to stop me to clarify.
Start by clarifying the definition of variance and whether the interviewer wants population or sample variance. Then implement a clean, efficient function that handles edge cases like empty lists and single-element lists, and discuss the time and space complexity. Be prepared to explain the difference between population and sample variance and when to use each.
Pro tip: Mention that for numerical stability, you can use a two-pass algorithm (compute mean first, then sum of squared deviations) or Welford's online algorithm for a single pass, especially for large datasets. This shows awareness of floating-point precision issues.
Ask whether to compute population variance (divide by N) or sample variance (divide by N-1). Confirm input assumptions: list of numbers, may be empty or have one element.
Decide between two-pass (compute mean, then sum of squared deviations) or one-pass (Welford's algorithm). Two-pass is simpler and usually sufficient; one-pass is more numerically stable and efficient for streaming data.
Write the function in Python, handling edge cases: empty list (raise ValueError or return None), single element (population variance 0, sample variance undefined). Use clear variable names and comments.
State time complexity O(n) and space complexity O(1) for both algorithms. Mention that two-pass requires two iterations but still O(n).
Explain when to use population vs sample variance, and the impact of numerical stability. Mention that for very large datasets, Welford's algorithm avoids catastrophic cancellation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.