[New-bugs-announce] [issue33573] statistics.median does not work with ordinal scale

[W deW]

New submission from W deW <felixfilicibus at gmail.com>:

The 0.5-quantile or median is defined for ordinal, interval, and ratio scales. An Enumerator as derived from Enum and extended with rich comparison methods implements an ordinal scale. Therefore calculating the median over a list of such enum-elements ought to be possible.

The current implementation tries to interpolate the median value by averaging the two middle observations. This is allowed for interval and ratio scales, but since this interpolation involves an addition, not so for ordinal scales. Although computationally it is possible to do this for numeric ordinal variables, logically it is non-sense for the distance between ordinal values is - by definition - unknown. On non-numeric ordinal values it is even computationally impossible.

The correct return value would be: the first value in an ordered set where al least half the number of observations is smaller or equal than it. This is observation[len(observation)//2] for odd and even length ordered lists of values.

Whether the same applies to interval and ratio scales is a matter of opinion. The currently implemented algorith definitely is more popular these days.

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components: Library (Lib)
files: testMedian.py
messages: 317048
nosy: W deW
priority: normal
severity: normal
status: open
title: statistics.median does not work with ordinal scale
type: crash
versions: Python 3.4
Added file: https://bugs.python.org/file47601/testMedian.py

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Python tracker <report at bugs.python.org>
<https://bugs.python.org/issue33573>
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