One pass only
Why it matters Sensors, logs and network taps produce data you see once. "Read it into a list first" is not an option, and the textbook formula for spread quietly breaks on the kind of numbers real systems produce.
A gateway on a factory floor watches a stream of readings and reports their count, mean, spread, minimum and maximum. It has a few kilobytes free and cannot rewind the stream. Some sensors report raw counters around one billion that only wobble by a few units.
Sample standard deviation: sqrt(sum((x - mean)^2) / (n - 1)), the usual "stdev". Written that way it needs the mean first, which means a second pass.
A famous one-pass shortcut uses the sum and the sum of squares. Try it on numbers near one billion before you trust it: subtracting two huge, nearly equal numbers leaves mostly rounding error.
Write stats(tape). tape is a Tape of floats. Return a dict with count, mean, stdev (sample, divide by n - 1; 0 for a single reading), min and max. With no readings: count 0 and None for the rest. Limits: read the tape once (20,000 reads for 20,000 readings); use at most 16,000 bytes of working memory (measured with tracemalloc); stdev must be within 1 part in a million of the true value, including for readings around 1,000,000,000 with a spread of about 10.
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