Add statistics.median_absolute_deviation#152227
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Add the median absolute deviation (MAD) function to the statistics module. MAD is a robust measure of statistical dispersion: the median of the absolute deviations from the median, optionally scaled by a consistency constant. The default scale=1.4826 (the consistency constant for the normal distribution) produces an estimator of the population standard deviation that is consistent with statistics.stdev. Pass scale=1.0 for the raw value. * data: a sequence or iterable of real-valued numbers * scale: int or float (Decimal/Fraction raise TypeError) Result type follows the data type (int/float input yields float; Decimal input yields Decimal; Fraction input yields Fraction). NaN propagates when at least one non-NaN value is present; all-NaN input raises StatisticsError (matching statistics.median()). Includes module docstring updates and __all__ entry.
Add TestMedianAbsoluteDeviation class in Lib/test/test_statistics.py, following the TestMedian / TestStdev pattern. Coverage: - Happy path: known answers for ints and floats, default / scale=1.0 / scale=2.0 / scale=3.0 / negative scale - Edge cases: empty (StatisticsError), single value, two-value symmetric, all-same, even-count averaging, generator input, tuple input - Error paths: non-numeric data (TypeError), all-NaN (StatisticsError), partial NaN (propagates) - Type acceptance: Decimal input -> Decimal result; Fraction input -> Fraction result (preserving precision); int input -> float result; mixed int+float -> float result - Scale type guard: Decimal / Fraction / str / list / None scale all raise TypeError Reuses NumericTestCase.assertApproxEqual for floating-point comparisons.
Document the new median_absolute_deviation function in Doc/library/statistics.rst: - Add :func:`median_absolute_deviation` to the 'Measures of spread' autosummary table - Add a new .. function:: directive with full description, doctest examples (int, Decimal, Fraction), and a .. versionadded:: 3.16 annotation
Add a new 'statistics' section under 'Improved modules' in Doc/whatsnew/3.16.rst, between shlex and tkinter (alphabetical order). Bullet describes the new statistics.median_absolute_deviation function, its default scale=1.4826 consistency constant, and the alternative scale=1 for the raw value. TODO: replace [REPLACE WITH CONTRIBUTOR NAME] and [REPLACE WITH PR NUMBER] placeholders with the actual contributor attribution when the PR is filed.
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Replace [REPLACE WITH CONTRIBUTOR NAME] and [REPLACE WITH PR NUMBER] placeholders with Anand Sundar and pythongh-152227 now that the PR is open.
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Replace [REPLACE WITH CONTRIBUTOR NAME] and [REPLACE WITH PR NUMBER] placeholders with Anand Sundar and pythongh-152227 now that the PR is open.
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Most changes to Python require a NEWS entry. Add one using the blurb_it web app or the blurb command-line tool. If this change has little impact on Python users, wait for a maintainer to apply the |
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Summary
Add
statistics.median_absolute_deviation(data, *, scale=1.4826)to the CPython standard library. The median absolute deviation (MAD) is the textbook robust measure of statistical dispersion: the median of the absolute deviations from the median.For normally distributed data, the default
scale=1.4826(the consistency constant) produces an estimator of the population standard deviation that is consistent withstatistics.stdev. Passscale=1.0for the raw value.Why
The
statisticsmodule currently provides traditional spread measures (variance,stdev) but lacks a robust counterpart. Standard deviation is well known to be sensitive to outliers; MAD is the textbook alternative. It is the default "robust scale" in R (mad()) and NumPy (median_abs_deviation). For users who don't want a third-party dependency for a single stat — educators, stdlib-only scripts, Python-first learners — stdlib MAD closes an obvious gap.What changes
Lib/statistics.py— newmedian_absolute_deviation(data, *, scale=1.4826)function. Result type follows input data (int/float → float; Decimal → Decimal; Fraction → Fraction).scalemust be int or float (Decimal/Fraction raiseTypeError). All-NaN input raisesStatisticsError; partial NaN propagates. Top docstring autosummary table and "Measures of spread" table widened to fit the 25-character name.__all__updated.Lib/test/test_statistics.py— newTestMedianAbsoluteDeviationclass with 28 test methods covering happy path, edge cases, error paths, type acceptance, and scale type guard. FollowsTestMedian/TestStdevpatterns.Doc/library/statistics.rst— autosummary table entry + full function directive with int/Decimal/Fraction doctest examples +.. versionadded:: 3.16.Doc/whatsnew/3.16.rst— new "statistics" section under "Improved modules".Out of scope (deliberately)
Lib/statistics.pyi— that file does not exist in CPython main. Type stubs for stdlib modules live in the separate typeshed repo and will be filed there as a follow-up. (grep -L '\.pyi' Lib/*.pyireturns zero matches inLib/.)NormalDistintegration — could be added asNormalDist.from_mad()in a follow-up PR if requested.TODO before merge
[REPLACE WITH CONTRIBUTOR NAME]and[REPLACE WITH PR NUMBER]placeholders in theDoc/whatsnew/3.16.rstentry.gh-XXXXXXplaceholders in the four commit messages with the actual issue/PR number (viagit rebase -i origin/mainandreword).median_absolute_deviation.