Easy

Welford Online Mean and Variance

Easy

~20 min

code completion

Welford Online Mean and Variance

Welford's algorithm computes mean and variance in a single pass, updating incrementally as each new value arrives. This is essential when data cannot be stored — it never materializes the full stream.

For each new value $x_{n}$ (1-indexed count n):

δ_{1} = x_{n} - μ_{n - 1}

μ_{n} = μ_{n - 1} + \frac{δ _{1}}{n}

δ_{2} = x_{n} - μ_{n}

M_{n} = M_{n - 1} + δ_{1} \times δ_{2}

At the end, population variance $= M_{n} / n$ .

Example: values = [2, 4, 4, 4, 5, 5, 7, 9]

Mean = 5.0, variance = 4.0 (population)

Your task:

Implement welford_mean_var(values) that returns (mean, variance) as a tuple of two floats.

Example Tests

Classic Welford example: mean=5.0, variance=4.0

Input: {"values":[2,4,4,4,5,5,7,9]}

Expected: [5,4]

All identical values: variance is 0

Input: {"values":[3,3,3,3]}

Expected: [3,0]

Two values: mean=3.0, variance=1.0 (population)

Input: {"values":[2,4]}

Expected: [3,1]

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