Weighted Mean, Variance and Survey Weights

Survey respondents and logged events often carry weights: one respondent may represent 500 people, another 2,000. Unweighted averages then give the wrong answer.

Implement:

• weighted_mean(x, w): $\sum w_i x_i / \sum w_i$
• weighted_var(x, w): the population-style weighted variance $\sum w_i (x_i - \bar x_w)^2 / \sum w_i$
• effective_sample_size(w): Kish's formula $(\sum w)^2 / \sum w^2$. Uneven weights mean less information than the raw count suggests.

Raise ValueError for negative weights, mismatched lengths, or weights that sum to 0.