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Compute Variance from a Python List

This question evaluates understanding of basic statistical concepts and numerical computation—specifically population versus sample variance—and tests algorithmic implementation skills, edge-case handling, and complexity reasoning within the Coding & Algorithms domain.

Given a Python list of numeric values, write a function to compute the variance without using external libraries such as NumPy or pandas.

Clarify any assumptions you make, such as:

whether you are computing population variance or sample variance,
how to handle an empty list or a list with one element,
and the expected time and space complexity.

Compute Population Variance from a Python List

Return population variance rounded to 6 decimals; return None for an empty list.

Examples

Example 1

Input: ([1,2,3],)
Output: 0.666667

Explanation: Population variance.

Example 2

Input: ([5,5,5],)
Output: 0.0

Explanation: Zero variance.

Hints

Model object-style prompts as arrays or operation streams when needed.
Handle empty and boundary cases before the main logic.