Reformat statistics.rst and remove unnecessary headings for each function.
This commit is contained in:
Georg Brandl
parent
a606542e95
commit
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@ -35,21 +35,34 @@ or sample.
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:func:`mode` Mode (most common value) of discrete data.
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======================= =============================================
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:func:`mean`
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~~~~~~~~~~~~
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Measures of spread
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------------------
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The :func:`mean` function calculates the arithmetic mean, commonly known
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as the average, of its iterable argument:
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These functions calculate a measure of how much the population or sample
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tends to deviate from the typical or average values.
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======================= =============================================
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:func:`pstdev` Population standard deviation of data.
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:func:`pvariance` Population variance of data.
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:func:`stdev` Sample standard deviation of data.
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:func:`variance` Sample variance of data.
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======================= =============================================
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Function details
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----------------
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.. function:: mean(data)
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Return the sample arithmetic mean of *data*, a sequence or iterator
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of real-valued numbers.
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Return the sample arithmetic mean of *data*, a sequence or iterator of
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real-valued numbers.
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The arithmetic mean is the sum of the data divided by the number of
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data points. It is commonly called "the average", although it is only
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one of many different mathematical averages. It is a measure of the
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central location of the data.
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The arithmetic mean is the sum of the data divided by the number of data
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points. It is commonly called "the average", although it is only one of many
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different mathematical averages. It is a measure of the central location of
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the data.
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If *data* is empty, :exc:`StatisticsError` will be raised.
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Some examples of use:
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@ -70,75 +83,56 @@ as the average, of its iterable argument:
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.. note::
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The mean is strongly effected by outliers and is not a robust
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estimator for central location: the mean is not necessarily a
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typical example of the data points. For more robust, although less
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efficient, measures of central location, see :func:`median` and
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:func:`mode`. (In this case, "efficient" refers to statistical
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efficiency rather than computational efficiency.)
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The mean is strongly effected by outliers and is not a robust estimator
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for central location: the mean is not necessarily a typical example of the
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data points. For more robust, although less efficient, measures of
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central location, see :func:`median` and :func:`mode`. (In this case,
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"efficient" refers to statistical efficiency rather than computational
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efficiency.)
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The sample mean gives an unbiased estimate of the true population
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mean, which means that, taken on average over all the possible
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samples, ``mean(sample)`` converges on the true mean of the entire
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population. If *data* represents the entire population rather than
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a sample, then ``mean(data)`` is equivalent to calculating the true
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population mean μ.
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The sample mean gives an unbiased estimate of the true population mean,
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which means that, taken on average over all the possible samples,
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``mean(sample)`` converges on the true mean of the entire population. If
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*data* represents the entire population rather than a sample, then
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``mean(data)`` is equivalent to calculating the true population mean μ.
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If ``data`` is empty, :exc:`StatisticsError` will be raised.
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:func:`median`
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~~~~~~~~~~~~~~
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The :func:`median` function calculates the median, or middle, data point,
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using the common "mean of middle two" method.
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.. seealso::
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:func:`median_low`
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:func:`median_high`
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:func:`median_grouped`
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.. function:: median(data)
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Return the median (middle value) of numeric data.
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Return the median (middle value) of numeric data, using the common "mean of
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middle two" method. If *data* is empty, :exc:`StatisticsError` is raised.
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The median is a robust measure of central location, and is less affected
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by the presence of outliers in your data. When the number of data points
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is odd, the middle data point is returned:
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The median is a robust measure of central location, and is less affected by
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the presence of outliers in your data. When the number of data points is
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odd, the middle data point is returned:
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.. doctest::
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>>> median([1, 3, 5])
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3
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When the number of data points is even, the median is interpolated by
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taking the average of the two middle values:
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When the number of data points is even, the median is interpolated by taking
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the average of the two middle values:
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.. doctest::
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>>> median([1, 3, 5, 7])
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4.0
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This is suited for when your data is discrete, and you don't mind that
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the median may not be an actual data point.
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This is suited for when your data is discrete, and you don't mind that the
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median may not be an actual data point.
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If data is empty, :exc:`StatisticsError` is raised.
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.. seealso:: :func:`median_low`, :func:`median_high`, :func:`median_grouped`
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:func:`median_low`
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~~~~~~~~~~~~~~~~~~
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The :func:`median_low` function calculates the low median without
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interpolation.
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.. function:: median_low(data)
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Return the low median of numeric data.
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Return the low median of numeric data. If *data* is empty,
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:exc:`StatisticsError` is raised.
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The low median is always a member of the data set. When the number
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of data points is odd, the middle value is returned. When it is
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even, the smaller of the two middle values is returned.
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The low median is always a member of the data set. When the number of data
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points is odd, the middle value is returned. When it is even, the smaller of
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the two middle values is returned.
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.. doctest::
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@ -147,24 +141,18 @@ interpolation.
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>>> median_low([1, 3, 5, 7])
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3
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Use the low median when your data are discrete and you prefer the median
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to be an actual data point rather than interpolated.
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Use the low median when your data are discrete and you prefer the median to
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be an actual data point rather than interpolated.
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If data is empty, :exc:`StatisticsError` is raised.
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:func:`median_high`
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~~~~~~~~~~~~~~~~~~~
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The :func:`median_high` function calculates the high median without
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interpolation.
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.. function:: median_high(data)
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Return the high median of data.
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Return the high median of data. If *data* is empty, :exc:`StatisticsError`
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is raised.
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The high median is always a member of the data set. When the number of
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data points is odd, the middle value is returned. When it is even, the
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larger of the two middle values is returned.
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The high median is always a member of the data set. When the number of data
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points is odd, the middle value is returned. When it is even, the larger of
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the two middle values is returned.
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.. doctest::
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@ -173,41 +161,34 @@ interpolation.
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>>> median_high([1, 3, 5, 7])
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5
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Use the high median when your data are discrete and you prefer the median
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to be an actual data point rather than interpolated.
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Use the high median when your data are discrete and you prefer the median to
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be an actual data point rather than interpolated.
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If data is empty, :exc:`StatisticsError` is raised.
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:func:`median_grouped`
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~~~~~~~~~~~~~~~~~~~~~~
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.. function:: median_grouped(data, interval=1)
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The :func:`median_grouped` function calculates the median of grouped data
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as the 50th percentile, using interpolation.
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.. function:: median_grouped(data [, interval])
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Return the median of grouped continuous data, calculated as the
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50th percentile.
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Return the median of grouped continuous data, calculated as the 50th
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percentile, using interpolation. If *data* is empty, :exc:`StatisticsError`
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is raised.
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.. doctest::
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>>> median_grouped([52, 52, 53, 54])
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52.5
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In the following example, the data are rounded, so that each value
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represents the midpoint of data classes, e.g. 1 is the midpoint of the
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class 0.5-1.5, 2 is the midpoint of 1.5-2.5, 3 is the midpoint of
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2.5-3.5, etc. With the data given, the middle value falls somewhere in
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the class 3.5-4.5, and interpolation is used to estimate it:
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In the following example, the data are rounded, so that each value represents
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the midpoint of data classes, e.g. 1 is the midpoint of the class 0.5-1.5, 2
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is the midpoint of 1.5-2.5, 3 is the midpoint of 2.5-3.5, etc. With the data
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given, the middle value falls somewhere in the class 3.5-4.5, and
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interpolation is used to estimate it:
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.. doctest::
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>>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
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3.7
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Optional argument ``interval`` represents the class interval, and
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defaults to 1. Changing the class interval naturally will change the
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interpolation:
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Optional argument *interval* represents the class interval, and defaults
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to 1. Changing the class interval naturally will change the interpolation:
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.. doctest::
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@ -217,36 +198,34 @@ as the 50th percentile, using interpolation.
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3.5
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This function does not check whether the data points are at least
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``interval`` apart.
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*interval* apart.
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.. impl-detail::
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Under some circumstances, :func:`median_grouped` may coerce data
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points to floats. This behaviour is likely to change in the future.
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Under some circumstances, :func:`median_grouped` may coerce data points to
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floats. This behaviour is likely to change in the future.
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.. seealso::
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* "Statistics for the Behavioral Sciences", Frederick J Gravetter
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and Larry B Wallnau (8th Edition).
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* "Statistics for the Behavioral Sciences", Frederick J Gravetter and
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Larry B Wallnau (8th Edition).
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* Calculating the `median <http://www.ualberta.ca/~opscan/median.html>`_.
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* The `SSMEDIAN <https://projects.gnome.org/gnumeric/doc/gnumeric-function-SSMEDIAN.shtml>`_
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function in the Gnome Gnumeric spreadsheet, including
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`this discussion <https://mail.gnome.org/archives/gnumeric-list/2011-April/msg00018.html>`_.
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* The `SSMEDIAN
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<https://projects.gnome.org/gnumeric/doc/gnumeric-function-SSMEDIAN.shtml>`_
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function in the Gnome Gnumeric spreadsheet, including `this discussion
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<https://mail.gnome.org/archives/gnumeric-list/2011-April/msg00018.html>`_.
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If data is empty, :exc:`StatisticsError` is raised.
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:func:`mode`
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~~~~~~~~~~~~
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The :func:`mode` function calculates the mode, or most common element, of
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discrete or nominal data. The mode (when it exists) is the most typical
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value, and is a robust measure of central location.
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.. function:: mode(data)
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Return the most common data point from discrete or nominal data.
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Return the most common data point from discrete or nominal *data*. The mode
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(when it exists) is the most typical value, and is a robust measure of
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central location.
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If *data* is empty, or if there is not exactly one most common value,
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:exc:`StatisticsError` is raised.
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``mode`` assumes discrete data, and returns a single value. This is the
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standard treatment of the mode as commonly taught in schools:
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@ -264,60 +243,35 @@ value, and is a robust measure of central location.
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>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
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'red'
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If data is empty, or if there is not exactly one most common value,
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:exc:`StatisticsError` is raised.
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Measures of spread
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------------------
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.. function:: pstdev(data, mu=None)
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These functions calculate a measure of how much the population or sample
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tends to deviate from the typical or average values.
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======================= =============================================
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:func:`pstdev` Population standard deviation of data.
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:func:`pvariance` Population variance of data.
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:func:`stdev` Sample standard deviation of data.
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:func:`variance` Sample variance of data.
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======================= =============================================
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:func:`pstdev`
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~~~~~~~~~~~~~~
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The :func:`pstdev` function calculates the standard deviation of a
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population. The standard deviation is equivalent to the square root of
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the variance.
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.. function:: pstdev(data [, mu])
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Return the square root of the population variance. See :func:`pvariance`
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for arguments and other details.
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Return the population standard deviation (the square root of the population
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variance). See :func:`pvariance` for arguments and other details.
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.. doctest::
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>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
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0.986893273527251
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:func:`pvariance`
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~~~~~~~~~~~~~~~~~
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The :func:`pvariance` function calculates the variance of a population.
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Variance, or second moment about the mean, is a measure of the variability
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(spread or dispersion) of data. A large variance indicates that the data is
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spread out; a small variance indicates it is clustered closely around the
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mean.
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.. function:: pvariance(data, mu=None)
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.. function:: pvariance(data [, mu])
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Return the population variance of *data*, a non-empty iterable of real-valued
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numbers. Variance, or second moment about the mean, is a measure of the
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variability (spread or dispersion) of data. A large variance indicates that
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the data is spread out; a small variance indicates it is clustered closely
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around the mean.
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Return the population variance of *data*, a non-empty iterable of
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real-valued numbers.
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If the optional second argument *mu* is given, it should be the mean
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of *data*. If it is missing or None (the default), the mean is
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If the optional second argument *mu* is given, it should be the mean of
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*data*. If it is missing or ``None`` (the default), the mean is
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automatically calculated.
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Use this function to calculate the variance from the entire population.
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To estimate the variance from a sample, the :func:`variance` function is
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usually a better choice.
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Use this function to calculate the variance from the entire population. To
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estimate the variance from a sample, the :func:`variance` function is usually
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a better choice.
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Raises :exc:`StatisticsError` if *data* is empty.
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Examples:
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@ -327,8 +281,8 @@ mean.
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>>> pvariance(data)
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1.25
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If you have already calculated the mean of your data, you can pass
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it as the optional second argument *mu* to avoid recalculation:
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If you have already calculated the mean of your data, you can pass it as the
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optional second argument *mu* to avoid recalculation:
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.. doctest::
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@ -336,9 +290,9 @@ mean.
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>>> pvariance(data, mu)
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1.25
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This function does not attempt to verify that you have passed the actual
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mean as *mu*. Using arbitrary values for *mu* may lead to invalid or
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impossible results.
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This function does not attempt to verify that you have passed the actual mean
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as *mu*. Using arbitrary values for *mu* may lead to invalid or impossible
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results.
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Decimals and Fractions are supported:
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@ -354,53 +308,44 @@ mean.
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.. note::
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When called with the entire population, this gives the population
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variance σ². When called on a sample instead, this is the biased
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sample variance s², also known as variance with N degrees of freedom.
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When called with the entire population, this gives the population variance
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σ². When called on a sample instead, this is the biased sample variance
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s², also known as variance with N degrees of freedom.
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If you somehow know the true population mean μ, you may use this
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function to calculate the variance of a sample, giving the known
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population mean as the second argument. Provided the data points are
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representative (e.g. independent and identically distributed), the
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result will be an unbiased estimate of the population variance.
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If you somehow know the true population mean μ, you may use this function
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to calculate the variance of a sample, giving the known population mean as
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the second argument. Provided the data points are representative
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(e.g. independent and identically distributed), the result will be an
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unbiased estimate of the population variance.
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Raises :exc:`StatisticsError` if *data* is empty.
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:func:`stdev`
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~~~~~~~~~~~~~~
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.. function:: stdev(data, xbar=None)
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The :func:`stdev` function calculates the standard deviation of a sample.
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The standard deviation is equivalent to the square root of the variance.
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.. function:: stdev(data [, xbar])
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Return the square root of the sample variance. See :func:`variance` for
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arguments and other details.
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Return the sample standard deviation (the square root of the sample
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variance). See :func:`variance` for arguments and other details.
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.. doctest::
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>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
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1.0810874155219827
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:func:`variance`
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~~~~~~~~~~~~~~~~~
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The :func:`variance` function calculates the variance of a sample. Variance,
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or second moment about the mean, is a measure of the variability (spread or
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dispersion) of data. A large variance indicates that the data is spread out;
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a small variance indicates it is clustered closely around the mean.
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.. function:: variance(data, xbar=None)
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.. function:: variance(data [, xbar])
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Return the sample variance of *data*, an iterable of at least two real-valued
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numbers. Variance, or second moment about the mean, is a measure of the
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variability (spread or dispersion) of data. A large variance indicates that
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the data is spread out; a small variance indicates it is clustered closely
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around the mean.
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Return the sample variance of *data*, an iterable of at least two
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real-valued numbers.
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If the optional second argument *xbar* is given, it should be the mean
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of *data*. If it is missing or None (the default), the mean is
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If the optional second argument *xbar* is given, it should be the mean of
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*data*. If it is missing or ``None`` (the default), the mean is
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automatically calculated.
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Use this function when your data is a sample from a population. To
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calculate the variance from the entire population, see :func:`pvariance`.
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Use this function when your data is a sample from a population. To calculate
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the variance from the entire population, see :func:`pvariance`.
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Raises :exc:`StatisticsError` if *data* has fewer than two values.
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Examples:
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@ -410,8 +355,8 @@ a small variance indicates it is clustered closely around the mean.
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>>> variance(data)
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1.3720238095238095
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If you have already calculated the mean of your data, you can pass
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it as the optional second argument *xbar* to avoid recalculation:
|
||||
If you have already calculated the mean of your data, you can pass it as the
|
||||
optional second argument *xbar* to avoid recalculation:
|
||||
|
||||
.. doctest::
|
||||
|
||||
|
|
@ -419,8 +364,8 @@ a small variance indicates it is clustered closely around the mean.
|
|||
>>> variance(data, m)
|
||||
1.3720238095238095
|
||||
|
||||
This function does not attempt to verify that you have passed the actual
|
||||
mean as *xbar*. Using arbitrary values for *xbar* can lead to invalid or
|
||||
This function does not attempt to verify that you have passed the actual mean
|
||||
as *xbar*. Using arbitrary values for *xbar* can lead to invalid or
|
||||
impossible results.
|
||||
|
||||
Decimal and Fraction values are supported:
|
||||
|
|
@ -437,17 +382,14 @@ a small variance indicates it is clustered closely around the mean.
|
|||
|
||||
.. note::
|
||||
|
||||
This is the sample variance s² with Bessel's correction, also known
|
||||
as variance with N-1 degrees of freedom. Provided that the data
|
||||
points are representative (e.g. independent and identically
|
||||
distributed), the result should be an unbiased estimate of the true
|
||||
population variance.
|
||||
This is the sample variance s² with Bessel's correction, also known as
|
||||
variance with N-1 degrees of freedom. Provided that the data points are
|
||||
representative (e.g. independent and identically distributed), the result
|
||||
should be an unbiased estimate of the true population variance.
|
||||
|
||||
If you somehow know the actual population mean μ you should pass it
|
||||
to the :func:`pvariance` function as the *mu* parameter to get
|
||||
the variance of a sample.
|
||||
|
||||
Raises :exc:`StatisticsError` if *data* has fewer than two values.
|
||||
If you somehow know the actual population mean μ you should pass it to the
|
||||
:func:`pvariance` function as the *mu* parameter to get the variance of a
|
||||
sample.
|
||||
|
||||
Exceptions
|
||||
----------
|
||||
|
|
|
|||
Loading…
Reference in New Issue