A Tale of Two Variances: Why NumPy and Pandas Give Different Answers

NumPy and Pandas return different variance values for the same dataset because they default to different formulas. NumPy defaults to population variance (divides by N, ddof=0), while Pandas defaults to sample variance (divides by N-1, ddof=1). The difference stems from Bessel's correction, which compensates for the bias introduced when estimating population variance from a sample. The post explains the math behind both formulas, the concept of degrees of freedom, and shows how to override defaults using the ddof parameter in NumPy, Pandas, Python's statistics module, and R.