How do you choose between statistics.mean, median, stdev and pstdev in Python?

## The module and the choice it forces `statistics` is the standard library's descriptive-summary module: pure Python, no dependency, working on any iterable of numbers. Its API splits along two axes that beginners routinely collapse into one. The first axis is *what kind of centre* you want, `mean` or `median`. The second is *what the data represents*: a sample (`stdev`, `variance`) or a complete population (`pstdev`, `pvariance`). Picking the wrong function on either axis produces a number that does not look wrong, which is exactly why the choice gets asked about. ## mean: every value votes `statistics.mean(data)` adds every value and divides by the count. Because every point contributes, one extreme value moves the result by roughly its own size divided by n. On five salaries where one is twenty times the rest, the mean lands above every ordinary value: ```pycon >>> import statistics >>> salaries = [42_000, 45_000, 47_000, 50_000, 900_000] >>> statistics.mean(salaries) 216800 ``` Two implementation details matter. `mean` does its arithmetic exactly, converting the input to `fractions.Fraction` internally, so it returns an `int` when the division comes out exact, a `float` when it does not, and a `Decimal` when fed `Decimal` input. That accuracy costs speed: `statistics.fmean(data)` converts to `float` up front and is far faster, and it accepts a `weights` argument. If what you actually want is an accurate *total* of many floats rather than an average, the tool next door on this subject is `math.fsum`. ## median: only the ordering votes `statistics.median(data)` sorts a copy and returns the middle value. On an even-length input it returns the average of the two middle values, which is why `statistics.median([1, 3, 5, 7])` is `4.0`, a value that is not in the data. When the answer must be a real data point, `statistics.median_low` and `statistics.median_high` return the lower or the upper of the two middles instead. Because only rank matters, replacing the largest value with something ten times larger does not move the median at all. That is the property you are buying: a summary that still describes the typical case when the tail is long. Request latencies with one timeout, response sizes with one huge payload, salaries with one founder in the list, all read honestly through the median and misleadingly through the mean. The rule of thumb to say out loud: roughly symmetric data where every point is meaningful, use `mean`; skewed data or known outliers, use `median`. And if the two disagree noticeably on the same list, that disagreement is itself the finding, so report both rather than picking the flattering one. ## stdev versus pstdev: the divisor is the whole difference Both compute the square root of the average squared deviation from the mean, and they differ only in what they divide by. `statistics.pstdev` divides the summed squared deviations by `n`. `statistics.stdev` divides by `n - 1`, known as Bessel's correction, because when the data is a *sample* drawn from a larger population the deviations are measured from the sample's own mean and therefore systematically understate how spread out the population is. `statistics.variance` and `statistics.pvariance` are the same pair without the square root. ```pycon >>> data = [2, 4, 4, 4, 5, 5, 7, 9] >>> statistics.pstdev(data) 2.0 >>> statistics.stdev(data) 2.138089935299395 ``` The gap shrinks as n grows and is negligible past a few hundred points, but at n = 8 it is about 7%. Choose by what the list literally *is*: every request the service handled in the last minute is the whole population of that minute, so `pstdev`; a thousand sampled requests standing in for millions is a sample, so `stdev`. Both functions accept a precomputed centre, `xbar=` for `stdev` and `mu=` for `pstdev`, so you do not recompute the mean when you already hold it; pass a centre that does not belong to the data and the result is silently wrong rather than an error. ## Errors, and the calls next to these four Every one of these functions raises `statistics.StatisticsError` instead of returning a sentinel when the input is too small. `statistics.mean([])` reports that it requires at least one data point, and `statistics.stdev([x])` reports that it requires at least two, because the `n - 1` divisor would be zero. `statistics.pstdev([x])` is legal and returns `0.0`. Guard the empty-list case at the call site rather than wrapping every call in `try`. Nearby in the same module and worth knowing so you do not reimplement them: `statistics.mode` returns the most common value, `statistics.multimode` returns every tied winner as a list, and `statistics.quantiles(data, n=4)` returns the cut points that split the data into n equally sized groups, which is what people often mean when they ask for the median and the quartiles together.