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bpo-35892: Fix mode() and add multimode() (#12089)

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Raymond Hettinger 2019-03-12 00:43:27 -07:00 committed by GitHub
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4 changed files with 97 additions and 48 deletions
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38
Doc/library/statistics.rst
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@ -37,7 +37,7 @@ Averages and measures of central location
These functions calculate an average or typical value from a population
or sample.
======================= =============================================
======================= ===============================================================
:func:`mean` Arithmetic mean ("average") of data.
:func:`fmean` Fast, floating point arithmetic mean.
:func:`harmonic_mean` Harmonic mean of data.
@ -45,8 +45,9 @@ or sample.
:func:`median_low` Low median of data.
:func:`median_high` High median of data.
:func:`median_grouped` Median, or 50th percentile, of grouped data.
:func:`mode` Mode (most common value) of discrete data.
======================= =============================================
:func:`mode` Single mode (most common value) of discrete or nominal data.
:func:`multimode` List of modes (most common values) of discrete or nomimal data.
======================= ===============================================================
Measures of spread
------------------
@ -287,12 +288,12 @@ However, for reading convenience, most of the examples show sorted sequences.
.. function:: mode(data)
Return the most common data point from discrete or nominal *data*. The mode
(when it exists) is the most typical value, and is a robust measure of
central location.
Return the single most common data point from discrete or nominal *data*.
The mode (when it exists) is the most typical value and serves as a
measure of central location.
If *data* is empty, or if there is not exactly one most common value,
:exc:`StatisticsError` is raised.
If there are multiple modes, returns the first one encountered in the *data*.
If *data* is empty, :exc:`StatisticsError` is raised.
``mode`` assumes discrete data, and returns a single value. This is the
standard treatment of the mode as commonly taught in schools:
@ -310,6 +311,27 @@ However, for reading convenience, most of the examples show sorted sequences.
>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
'red'
.. versionchanged:: 3.8
Now handles multimodal datasets by returning the first mode encountered.
Formerly, it raised :exc:`StatisticsError` when more than one mode was
found.
.. function:: multimode(data)
Return a list of the most frequently occurring values in the order they
were first encountered in the *data*. Will return more than one result if
there are multiple modes or an empty list if the *data* is empty:
.. doctest::
>>> multimode('aabbbbccddddeeffffgg')
['b', 'd', 'f']
>>> multimode('')
[]
.. versionadded:: 3.8
.. function:: pstdev(data, mu=None)

8
Doc/whatsnew/3.8.rst
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@ -282,6 +282,9 @@ Added :func:`statistics.fmean` as a faster, floating point variant of
:func:`statistics.mean()`. (Contributed by Raymond Hettinger and
Steven D'Aprano in :issue:`35904`.)
Added :func:`statistics.multimode` that returns a list of the most
common values. (Contributed by Raymond Hettinger in :issue:`35892`.)
Added :class:`statistics.NormalDist`, a tool for creating
and manipulating normal distributions of a random variable.
(Contributed by Raymond Hettinger in :issue:`36018`.)
@ -591,6 +594,11 @@ Changes in the Python API
* The function :func:`platform.popen` has been removed, it was deprecated since
Python 3.3: use :func:`os.popen` instead.
* The :func:`statistics.mode` function no longer raises an exception
when given multimodal data. Instead, it returns the first mode
encountered in the input data. (Contributed by Raymond Hettinger
in :issue:`35892`.)
* The :meth:`~tkinter.ttk.Treeview.selection` method of the
:class:`tkinter.ttk.Treeview` class no longer takes arguments. Using it with
arguments for changing the selection was deprecated in Python 3.6. Use

72
Lib/statistics.py
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@ -17,6 +17,7 @@ median_low Low median of data.
median_high High median of data.
median_grouped Median, or 50th percentile, of grouped data.
mode Mode (most common value) of data.
multimode List of modes (most common values of data)
================== =============================================
Calculate the arithmetic mean ("the average") of data:
@ -79,10 +80,9 @@ A single exception is defined: StatisticsError is a subclass of ValueError.
__all__ = [ 'StatisticsError', 'NormalDist',
'pstdev', 'pvariance', 'stdev', 'variance',
'median', 'median_low', 'median_high', 'median_grouped',
'mean', 'mode', 'harmonic_mean', 'fmean',
'mean', 'mode', 'multimode', 'harmonic_mean', 'fmean',
]
import collections
import math
import numbers
import random
@ -92,8 +92,8 @@ from decimal import Decimal
from itertools import groupby
from bisect import bisect_left, bisect_right
from math import hypot, sqrt, fabs, exp, erf, tau, log, fsum
from operator import itemgetter
from collections import Counter
# === Exceptions ===
@ -249,20 +249,6 @@ def _convert(value, T):
raise
def _counts(data):
# Generate a table of sorted (value, frequency) pairs.
table = collections.Counter(iter(data)).most_common()
if not table:
return table
# Extract the values with the highest frequency.
maxfreq = table[0][1]
for i in range(1, len(table)):
if table[i][1] != maxfreq:
table = table[:i]
break
return table
def _find_lteq(a, x):
'Locate the leftmost value exactly equal to x'
i = bisect_left(a, x)
@ -334,9 +320,9 @@ def fmean(data):
nonlocal n
n += 1
return x
total = math.fsum(map(count, data))
total = fsum(map(count, data))
else:
total = math.fsum(data)
total = fsum(data)
try:
return total / n
except ZeroDivisionError:
@ -523,19 +509,38 @@ def mode(data):
>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
'red'
If there is not exactly one most common value, ``mode`` will raise
StatisticsError.
If there are multiple modes, return the first one encountered.
>>> mode(['red', 'red', 'green', 'blue', 'blue'])
'red'
If *data* is empty, ``mode``, raises StatisticsError.
"""
# Generate a table of sorted (value, frequency) pairs.
table = _counts(data)
if len(table) == 1:
return table[0][0]
elif table:
raise StatisticsError(
'no unique mode; found %d equally common values' % len(table)
)
else:
raise StatisticsError('no mode for empty data')
data = iter(data)
try:
return Counter(data).most_common(1)[0][0]
except IndexError:
raise StatisticsError('no mode for empty data') from None
def multimode(data):
""" Return a list of the most frequently occurring values.
Will return more than one result if there are multiple modes
or an empty list if *data* is empty.
>>> multimode('aabbbbbbbbcc')
['b']
>>> multimode('aabbbbccddddeeffffgg')
['b', 'd', 'f']
>>> multimode('')
[]
"""
counts = Counter(iter(data)).most_common()
maxcount, mode_items = next(groupby(counts, key=itemgetter(1)), (0, []))
return list(map(itemgetter(0), mode_items))
# === Measures of spread ===
@ -836,6 +841,7 @@ if __name__ == '__main__':
from math import isclose
from operator import add, sub, mul, truediv
from itertools import repeat
import doctest
g1 = NormalDist(10, 20)
g2 = NormalDist(-5, 25)
@ -893,3 +899,5 @@ if __name__ == '__main__':
S = NormalDist.from_samples([x - y for x, y in zip(X.samples(n),
Y.samples(n))])
assert_close(X - Y, S)
print(doctest.testmod())

27
Lib/test/test_statistics.py
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@ -1769,7 +1769,7 @@ class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin):
def test_range_data(self):
# Override test from UnivariateCommonMixin.
data = range(20, 50, 3)
self.assertRaises(statistics.StatisticsError, self.func, data)
self.assertEqual(self.func(data), 20)
def test_nominal_data(self):
# Test mode with nominal data.
@ -1790,13 +1790,14 @@ class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin):
# Test mode with bimodal data.
data = [1, 1, 2, 2, 2, 2, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9]
assert data.count(2) == data.count(6) == 4
# Check for an exception.
self.assertRaises(statistics.StatisticsError, self.func, data)
# mode() should return 2, the first encounted mode
self.assertEqual(self.func(data), 2)
def test_unique_data_failure(self):
# Test mode exception when data points are all unique.
def test_unique_data(self):
# Test mode when data points are all unique.
data = list(range(10))
self.assertRaises(statistics.StatisticsError, self.func, data)
# mode() should return 0, the first encounted mode
self.assertEqual(self.func(data), 0)
def test_none_data(self):
# Test that mode raises TypeError if given None as data.
@ -1809,8 +1810,18 @@ class TestMode(NumericTestCase, AverageMixin, UnivariateTypeMixin):
# Test that a Counter is treated like any other iterable.
data = collections.Counter([1, 1, 1, 2])
# Since the keys of the counter are treated as data points, not the
# counts, this should raise.
self.assertRaises(statistics.StatisticsError, self.func, data)
# counts, this should return the first mode encountered, 1
self.assertEqual(self.func(data), 1)
class TestMultiMode(unittest.TestCase):
def test_basics(self):
multimode = statistics.multimode
self.assertEqual(multimode('aabbbbbbbbcc'), ['b'])
self.assertEqual(multimode('aabbbbccddddeeffffgg'), ['b', 'd', 'f'])
self.assertEqual(multimode(''), [])
class TestFMean(unittest.TestCase):