Rolling Mean and Variance: When to Use It

Start with the idea

A problem is a good match for Rolling Mean and Variance when it asks for telemetry, anomaly windows, streaming statistics. Here the concrete task is: Return integer means for windows of length three. The visible input [2,4,6,8,10] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Choose this family when a valid window can be repaired by moving one boundary; non-monotone constraints may need a different method. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Update sufficient statistics as samples enter and leave rather than retaining every computation. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? A window is a contiguous interval with a maintained summary. Describe what entering the right edge adds and what leaving the left edge removes. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(n) time · O(k) storage for eviction; identify the operation responsible for it and the extra memory it needs.