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#: ../Doc/library/statistics.rst:2
msgid ":mod:`statistics` --- Mathematical statistics functions"
msgstr ""

#: ../Doc/library/statistics.rst:12
msgid "**Source code:** :source:`Lib/statistics.py`"
msgstr "**Code source :** :source:`Lib/statistics.py`"

#: ../Doc/library/statistics.rst:21
msgid ""
"This module provides functions for calculating mathematical statistics of "
"numeric (:class:`Real`-valued) data."
msgstr ""

#: ../Doc/library/statistics.rst:26
msgid ""
"Unless explicitly noted otherwise, these functions support :class:`int`, :"
"class:`float`, :class:`decimal.Decimal` and :class:`fractions.Fraction`. "
"Behaviour with other types (whether in the numeric tower or not) is "
"currently unsupported.  Mixed types are also undefined and implementation-"
"dependent.  If your input data consists of mixed types, you may be able to "
"use :func:`map` to ensure a consistent result, e.g. ``map(float, "
"input_data)``."
msgstr ""

#: ../Doc/library/statistics.rst:35
msgid "Averages and measures of central location"
msgstr ""

#: ../Doc/library/statistics.rst:37
msgid ""
"These functions calculate an average or typical value from a population or "
"sample."
msgstr ""

#: ../Doc/library/statistics.rst:41
msgid ":func:`mean`"
msgstr ""

#: ../Doc/library/statistics.rst:41
msgid "Arithmetic mean (\"average\") of data."
msgstr ""

#: ../Doc/library/statistics.rst:42
msgid ":func:`harmonic_mean`"
msgstr ""

#: ../Doc/library/statistics.rst:42
msgid "Harmonic mean of data."
msgstr ""

#: ../Doc/library/statistics.rst:43
msgid ":func:`median`"
msgstr ""

#: ../Doc/library/statistics.rst:43
msgid "Median (middle value) of data."
msgstr ""

#: ../Doc/library/statistics.rst:44
msgid ":func:`median_low`"
msgstr ""

#: ../Doc/library/statistics.rst:44
msgid "Low median of data."
msgstr ""

#: ../Doc/library/statistics.rst:45
msgid ":func:`median_high`"
msgstr ""

#: ../Doc/library/statistics.rst:45
msgid "High median of data."
msgstr ""

#: ../Doc/library/statistics.rst:46
msgid ":func:`median_grouped`"
msgstr ""

#: ../Doc/library/statistics.rst:46
msgid "Median, or 50th percentile, of grouped data."
msgstr ""

#: ../Doc/library/statistics.rst:47
msgid ":func:`mode`"
msgstr ""

#: ../Doc/library/statistics.rst:47
msgid "Mode (most common value) of discrete data."
msgstr ""

#: ../Doc/library/statistics.rst:51
msgid "Measures of spread"
msgstr ""

#: ../Doc/library/statistics.rst:53
msgid ""
"These functions calculate a measure of how much the population or sample "
"tends to deviate from the typical or average values."
msgstr ""

#: ../Doc/library/statistics.rst:57
msgid ":func:`pstdev`"
msgstr ""

#: ../Doc/library/statistics.rst:57
msgid "Population standard deviation of data."
msgstr ""

#: ../Doc/library/statistics.rst:58
msgid ":func:`pvariance`"
msgstr ""

#: ../Doc/library/statistics.rst:58
msgid "Population variance of data."
msgstr ""

#: ../Doc/library/statistics.rst:59
msgid ":func:`stdev`"
msgstr ""

#: ../Doc/library/statistics.rst:59
msgid "Sample standard deviation of data."
msgstr ""

#: ../Doc/library/statistics.rst:60
msgid ":func:`variance`"
msgstr ""

#: ../Doc/library/statistics.rst:60
msgid "Sample variance of data."
msgstr ""

#: ../Doc/library/statistics.rst:65
msgid "Function details"
msgstr ""

#: ../Doc/library/statistics.rst:67
msgid ""
"Note: The functions do not require the data given to them to be sorted. "
"However, for reading convenience, most of the examples show sorted sequences."
msgstr ""

#: ../Doc/library/statistics.rst:72
msgid ""
"Return the sample arithmetic mean of *data* which can be a sequence or "
"iterator."
msgstr ""

#: ../Doc/library/statistics.rst:74
msgid ""
"The arithmetic mean is the sum of the data divided by the number of data "
"points.  It is commonly called \"the average\", although it is only one of "
"many different mathematical averages.  It is a measure of the central "
"location of the data."
msgstr ""

#: ../Doc/library/statistics.rst:79
msgid "If *data* is empty, :exc:`StatisticsError` will be raised."
msgstr ""

#: ../Doc/library/statistics.rst:81
msgid "Some examples of use:"
msgstr ""

#: ../Doc/library/statistics.rst:100
msgid ""
"The mean is strongly affected by outliers and is not a robust estimator for "
"central location: the mean is not necessarily a typical example of the data "
"points.  For more robust, although less efficient, measures of central "
"location, see :func:`median` and :func:`mode`.  (In this case, \"efficient\" "
"refers to statistical efficiency rather than computational efficiency.)"
msgstr ""

#: ../Doc/library/statistics.rst:107
msgid ""
"The sample mean gives an unbiased estimate of the true population mean, "
"which means that, taken on average over all the possible samples, "
"``mean(sample)`` converges on the true mean of the entire population.  If "
"*data* represents the entire population rather than a sample, then "
"``mean(data)`` is equivalent to calculating the true population mean μ."
msgstr ""

#: ../Doc/library/statistics.rst:116
msgid ""
"Return the harmonic mean of *data*, a sequence or iterator of real-valued "
"numbers."
msgstr ""

#: ../Doc/library/statistics.rst:119
msgid ""
"The harmonic mean, sometimes called the subcontrary mean, is the reciprocal "
"of the arithmetic :func:`mean` of the reciprocals of the data. For example, "
"the harmonic mean of three values *a*, *b* and *c* will be equivalent to ``3/"
"(1/a + 1/b + 1/c)``."
msgstr ""

#: ../Doc/library/statistics.rst:124
msgid ""
"The harmonic mean is a type of average, a measure of the central location of "
"the data.  It is often appropriate when averaging quantities which are rates "
"or ratios, for example speeds. For example:"
msgstr ""

#: ../Doc/library/statistics.rst:128
msgid ""
"Suppose an investor purchases an equal value of shares in each of three "
"companies, with P/E (price/earning) ratios of 2.5, 3 and 10. What is the "
"average P/E ratio for the investor's portfolio?"
msgstr ""

#: ../Doc/library/statistics.rst:137
msgid ""
"Using the arithmetic mean would give an average of about 5.167, which is too "
"high."
msgstr ""

#: ../Doc/library/statistics.rst:140
msgid ""
":exc:`StatisticsError` is raised if *data* is empty, or any element is less "
"than zero."
msgstr ""

#: ../Doc/library/statistics.rst:148
msgid ""
"Return the median (middle value) of numeric data, using the common \"mean of "
"middle two\" method.  If *data* is empty, :exc:`StatisticsError` is raised. "
"*data* can be a sequence or iterator."
msgstr ""

#: ../Doc/library/statistics.rst:152
msgid ""
"The median is a robust measure of central location, and is less affected by "
"the presence of outliers in your data.  When the number of data points is "
"odd, the middle data point is returned:"
msgstr ""

#: ../Doc/library/statistics.rst:161
msgid ""
"When the number of data points is even, the median is interpolated by taking "
"the average of the two middle values:"
msgstr ""

#: ../Doc/library/statistics.rst:169
msgid ""
"This is suited for when your data is discrete, and you don't mind that the "
"median may not be an actual data point."
msgstr ""

#: ../Doc/library/statistics.rst:172
msgid ""
"If your data is ordinal (supports order operations) but not numeric (doesn't "
"support addition), you should use :func:`median_low` or :func:`median_high` "
"instead."
msgstr ""

#: ../Doc/library/statistics.rst:176
msgid ":func:`median_low`, :func:`median_high`, :func:`median_grouped`"
msgstr ""

#: ../Doc/library/statistics.rst:181
msgid ""
"Return the low median of numeric data.  If *data* is empty, :exc:"
"`StatisticsError` is raised.  *data* can be a sequence or iterator."
msgstr ""

#: ../Doc/library/statistics.rst:184
msgid ""
"The low median is always a member of the data set.  When the number of data "
"points is odd, the middle value is returned.  When it is even, the smaller "
"of the two middle values is returned."
msgstr ""

#: ../Doc/library/statistics.rst:195
msgid ""
"Use the low median when your data are discrete and you prefer the median to "
"be an actual data point rather than interpolated."
msgstr ""

#: ../Doc/library/statistics.rst:201
msgid ""
"Return the high median of data.  If *data* is empty, :exc:`StatisticsError` "
"is raised.  *data* can be a sequence or iterator."
msgstr ""

#: ../Doc/library/statistics.rst:204
msgid ""
"The high median is always a member of the data set.  When the number of data "
"points is odd, the middle value is returned.  When it is even, the larger of "
"the two middle values is returned."
msgstr ""

#: ../Doc/library/statistics.rst:215
msgid ""
"Use the high median when your data are discrete and you prefer the median to "
"be an actual data point rather than interpolated."
msgstr ""

#: ../Doc/library/statistics.rst:221
msgid ""
"Return the median of grouped continuous data, calculated as the 50th "
"percentile, using interpolation.  If *data* is empty, :exc:`StatisticsError` "
"is raised.  *data* can be a sequence or iterator."
msgstr ""

#: ../Doc/library/statistics.rst:230
msgid ""
"In the following example, the data are rounded, so that each value "
"represents the midpoint of data classes, e.g. 1 is the midpoint of the class "
"0.5--1.5, 2 is the midpoint of 1.5--2.5, 3 is the midpoint of 2.5--3.5, "
"etc.  With the data given, the middle value falls somewhere in the class "
"3.5--4.5, and interpolation is used to estimate it:"
msgstr ""

#: ../Doc/library/statistics.rst:241
msgid ""
"Optional argument *interval* represents the class interval, and defaults to "
"1.  Changing the class interval naturally will change the interpolation:"
msgstr ""

#: ../Doc/library/statistics.rst:251
msgid ""
"This function does not check whether the data points are at least *interval* "
"apart."
msgstr ""

#: ../Doc/library/statistics.rst:256
msgid ""
"Under some circumstances, :func:`median_grouped` may coerce data points to "
"floats.  This behaviour is likely to change in the future."
msgstr ""

#: ../Doc/library/statistics.rst:261
msgid ""
"\"Statistics for the Behavioral Sciences\", Frederick J Gravetter and Larry "
"B Wallnau (8th Edition)."
msgstr ""

#: ../Doc/library/statistics.rst:264
msgid ""
"The `SSMEDIAN <https://help.gnome.org/users/gnumeric/stable/gnumeric."
"html#gnumeric-function-SSMEDIAN>`_ function in the Gnome Gnumeric "
"spreadsheet, including `this discussion <https://mail.gnome.org/archives/"
"gnumeric-list/2011-April/msg00018.html>`_."
msgstr ""

#: ../Doc/library/statistics.rst:272
msgid ""
"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."
msgstr ""

#: ../Doc/library/statistics.rst:276
msgid ""
"If *data* is empty, or if there is not exactly one most common value, :exc:"
"`StatisticsError` is raised."
msgstr ""

#: ../Doc/library/statistics.rst:279
msgid ""
"``mode`` assumes discrete data, and returns a single value. This is the "
"standard treatment of the mode as commonly taught in schools:"
msgstr ""

#: ../Doc/library/statistics.rst:287
msgid ""
"The mode is unique in that it is the only statistic which also applies to "
"nominal (non-numeric) data:"
msgstr ""

#: ../Doc/library/statistics.rst:298
msgid ""
"Return the population standard deviation (the square root of the population "
"variance).  See :func:`pvariance` for arguments and other details."
msgstr ""

#: ../Doc/library/statistics.rst:309
msgid ""
"Return the population variance of *data*, a non-empty iterable of real-"
"valued numbers.  Variance, or second moment about the mean, is a measure of "
"the variability (spread or dispersion) of data.  A large variance indicates "
"that the data is spread out; a small variance indicates it is clustered "
"closely around the mean."
msgstr ""

#: ../Doc/library/statistics.rst:315
msgid ""
"If the optional second argument *mu* is given, it should be the mean of "
"*data*.  If it is missing or ``None`` (the default), the mean is "
"automatically calculated."
msgstr ""

#: ../Doc/library/statistics.rst:319
msgid ""
"Use this function to calculate the variance from the entire population.  To "
"estimate the variance from a sample, the :func:`variance` function is "
"usually a better choice."
msgstr ""

#: ../Doc/library/statistics.rst:323
msgid "Raises :exc:`StatisticsError` if *data* is empty."
msgstr ""

#: ../Doc/library/statistics.rst:325 ../Doc/library/statistics.rst:399
msgid "Examples:"
msgstr "Exemples : ::"

#: ../Doc/library/statistics.rst:333
msgid ""
"If you have already calculated the mean of your data, you can pass it as the "
"optional second argument *mu* to avoid recalculation:"
msgstr ""

#: ../Doc/library/statistics.rst:342
msgid ""
"This function does not attempt to verify that you have passed the actual "
"mean as *mu*.  Using arbitrary values for *mu* may lead to invalid or "
"impossible results."
msgstr ""

#: ../Doc/library/statistics.rst:346
msgid "Decimals and Fractions are supported:"
msgstr ""

#: ../Doc/library/statistics.rst:360
msgid ""
"When called with the entire population, this gives the population variance "
"σ².  When called on a sample instead, this is the biased sample variance s², "
"also known as variance with N degrees of freedom."
msgstr ""

#: ../Doc/library/statistics.rst:364
msgid ""
"If you somehow know the true population mean μ, you may use this function to "
"calculate the variance of a sample, giving the known population mean as the "
"second argument.  Provided the data points are representative (e.g. "
"independent and identically distributed), the result will be an unbiased "
"estimate of the population variance."
msgstr ""

#: ../Doc/library/statistics.rst:373
msgid ""
"Return the sample standard deviation (the square root of the sample "
"variance).  See :func:`variance` for arguments and other details."
msgstr ""

#: ../Doc/library/statistics.rst:384
msgid ""
"Return the sample variance of *data*, an iterable of at least two real-"
"valued numbers.  Variance, or second moment about the mean, is a measure of "
"the variability (spread or dispersion) of data.  A large variance indicates "
"that the data is spread out; a small variance indicates it is clustered "
"closely around the mean."
msgstr ""

#: ../Doc/library/statistics.rst:390
msgid ""
"If the optional second argument *xbar* is given, it should be the mean of "
"*data*.  If it is missing or ``None`` (the default), the mean is "
"automatically calculated."
msgstr ""

#: ../Doc/library/statistics.rst:394
msgid ""
"Use this function when your data is a sample from a population. To calculate "
"the variance from the entire population, see :func:`pvariance`."
msgstr ""

#: ../Doc/library/statistics.rst:397
msgid "Raises :exc:`StatisticsError` if *data* has fewer than two values."
msgstr ""

#: ../Doc/library/statistics.rst:407
msgid ""
"If you have already calculated the mean of your data, you can pass it as the "
"optional second argument *xbar* to avoid recalculation:"
msgstr ""

#: ../Doc/library/statistics.rst:416
msgid ""
"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."
msgstr ""

#: ../Doc/library/statistics.rst:420
msgid "Decimal and Fraction values are supported:"
msgstr ""

#: ../Doc/library/statistics.rst:434
msgid ""
"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."
msgstr ""

#: ../Doc/library/statistics.rst:439
msgid ""
"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."
msgstr ""

#: ../Doc/library/statistics.rst:444
msgid "Exceptions"
msgstr "Exceptions"

#: ../Doc/library/statistics.rst:446
msgid "A single exception is defined:"
msgstr ""

#: ../Doc/library/statistics.rst:450
msgid "Subclass of :exc:`ValueError` for statistics-related exceptions."
msgstr ""
