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Learn Welford's algorithm
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Module 2
Welford's Algorithm: Derivation and Properties
1
Welford's Algorithm: Mean Update Rule
Derive the recursive update rule for the mean used in Welford's algorithm.
2
Recursive Update for Sum of Squared Differences
Derive the recursive update rule for the sum of squared differences from the mean (M_k).
3
Numerical Stability of Welford's Algorithm
Explain why Welford's algorithm avoids catastrophic cancellation and maintains numerical stability.
Previous module
The Challenge of Numerical Stability in Variance Calculation
Next module
Practical Implementation and Empirical Comparison