Compute variance of a list in Python

Task

Given a Python list of numbers (ints/floats), write code to compute its variance.

Requirements

• Input: nums: list[float] (length $n\ge 1$ )
• Clarify whether you are computing:
  • Population variance : $\sigma^2 = \frac{1}{n}\sum_{i=1}^n (x_i-\bar{x})^2$ , or
  • Sample variance : $s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i-\bar{x})^2$ (requires $n\ge 2$ )
• Avoid using numpy / pandas unless explicitly allowed.
• State time and space complexity.

Follow-ups (optional)

• Implement a numerically stable one-pass version.
• Handle edge cases (empty list, single element, very large numbers).