Differentiate sample vs population standard deviation
Overview
This question evaluates understanding of statistical concepts such as population versus sample standard deviation and Bessel’s correction, along with practical competencies in implementing rolling time-series computations, handling edge cases like k=1, and documenting/configuring implementation choices in the Statistics & Math domain.
DRW
Aug 9, 2025, 12:00 AM
Data Scientist
Technical Screen
Statistics & Math
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Population vs. Sample Standard Deviation in a Finite Rolling Window
Context
You are implementing a rolling standard deviation over a fixed-size window of length k for a time series. Clarify how to compute standard deviation within each window, which denominator to use and why, how that choice impacts rolling estimates (especially for small k), what to return when k = 1, and how to expose and document this choice in code and tests.
Tasks
- Differentiate population vs. sample standard deviation for a finite window and explain why the denominators are n and n−1 (Bessel’s correction).
- Explain how this choice affects rolling estimates, especially for small k.
- Specify what the function should return for k = 1.
- State which definition you would implement by default, how to make it configurable, and how to document the choice in code and tests.
Solution
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