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Files and Folders in: //opt/alt/python312/lib64/python3.12/__pycache__/

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Reading File: //opt/alt/python312/lib64/python3.12/__pycache__//statistics.cpython-312.pyc

�

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�de#�Z$d�Z%dCd�Z&d�Z'd�Z(d�Z)d�Z*dDd�Z+ddddd�de,e-fd�Z.de/de/de/fd�Z0dejbjdzd zZ3e/e4d!<de/de/de-fd"�Z5de/de/de	fd#�Z6d$�Z7dCd%�Z8d&�Z9dCd'�Z:d(�Z;d)�Z<d*�Z=dEd+�Z>d,�Z?d-�Z@d.d/d0�d1�ZAdCd2�ZBdCd3�ZCdCd4�ZDdCd5�ZEd6�ZFd7�ZGd8d9�d:�ZHe d;d<�ZIdd=�d>�ZJd?�ZK	dd@lLmKZKGdA�dB�ZNy#eM$rY�wxYw)Fa�

Basic statistics module.

This module provides functions for calculating statistics of data, including
averages, variance, and standard deviation.

Calculating averages
--------------------

==================  ==================================================
Function            Description
==================  ==================================================
mean                Arithmetic mean (average) of data.
fmean               Fast, floating-point arithmetic mean.
geometric_mean      Geometric mean of data.
harmonic_mean       Harmonic mean of data.
median              Median (middle value) of data.
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).
quantiles           Divide data into intervals with equal probability.
==================  ==================================================

Calculate the arithmetic mean ("the average") of data:

>>> mean([-1.0, 2.5, 3.25, 5.75])
2.625


Calculate the standard median of discrete data:

>>> median([2, 3, 4, 5])
3.5


Calculate the median, or 50th percentile, of data grouped into class intervals
centred on the data values provided. E.g. if your data points are rounded to
the nearest whole number:

>>> median_grouped([2, 2, 3, 3, 3, 4])  #doctest: +ELLIPSIS
2.8333333333...

This should be interpreted in this way: you have two data points in the class
interval 1.5-2.5, three data points in the class interval 2.5-3.5, and one in
the class interval 3.5-4.5. The median of these data points is 2.8333...


Calculating variability or spread
---------------------------------

==================  =============================================
Function            Description
==================  =============================================
pvariance           Population variance of data.
variance            Sample variance of data.
pstdev              Population standard deviation of data.
stdev               Sample standard deviation of data.
==================  =============================================

Calculate the standard deviation of sample data:

>>> stdev([2.5, 3.25, 5.5, 11.25, 11.75])  #doctest: +ELLIPSIS
4.38961843444...

If you have previously calculated the mean, you can pass it as the optional
second argument to the four "spread" functions to avoid recalculating it:

>>> data = [1, 2, 2, 4, 4, 4, 5, 6]
>>> mu = mean(data)
>>> pvariance(data, mu)
2.5


Statistics for relations between two inputs
-------------------------------------------

==================  ====================================================
Function            Description
==================  ====================================================
covariance          Sample covariance for two variables.
correlation         Pearson's correlation coefficient for two variables.
linear_regression   Intercept and slope for simple linear regression.
==================  ====================================================

Calculate covariance, Pearson's correlation, and simple linear regression
for two inputs:

>>> x = [1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
>>> covariance(x, y)
0.75
>>> correlation(x, y)  #doctest: +ELLIPSIS
0.31622776601...
>>> linear_regression(x, y)  #doctest:
LinearRegression(slope=0.1, intercept=1.5)


Exceptions
----------

A single exception is defined: StatisticsError is a subclass of ValueError.

)�
NormalDist�StatisticsError�correlation�
covariance�fmean�geometric_mean�
harmonic_mean�linear_regression�mean�median�median_grouped�median_high�
median_low�mode�	multimode�pstdev�	pvariance�	quantiles�stdev�variance�N��Fraction)�Decimal)�count�groupby�repeat)�bisect_left�bisect_right)	�hypot�sqrt�fabs�exp�erf�tau�log�fsum�sumprod)�reduce)�
itemgetter)�Counter�
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__module__�__qualname__���1/opt/alt/python312/lib64/python3.12/statistics.pyrr�s��r3rc��d}t�}|j}i}|j}t|t�D]9\}}||�tt|�D]\}}	|dz
}||	d�|z||	<��;d|vr|d}
t|
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tt|t�}||
|fS)a�_sum(data) -> (type, sum, count)

    Return a high-precision sum of the given numeric data as a fraction,
    together with the type to be converted to and the count of items.

    Examples
    --------

    >>> _sum([3, 2.25, 4.5, -0.5, 0.25])
    (<class 'float'>, Fraction(19, 2), 5)

    Some sources of round-off error will be avoided:

    # Built-in sum returns zero.
    >>> _sum([1e50, 1, -1e50] * 1000)
    (<class 'float'>, Fraction(1000, 1), 3000)

    Fractions and Decimals are also supported:

    >>> from fractions import Fraction as F
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    (<class 'fractions.Fraction'>, Fraction(63, 20), 4)

    >>> from decimal import Decimal as D
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        >>> _rank(goals, key=itemgetter(1), reverse=True)
        [2.0, 1.0, 3.0]

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    Fraction(13, 21)

    >>> from decimal import Decimal as D
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        >>> harmonic_mean([40, 60])
        48.0

    Suppose a car travels 40 km/hr for 5 km, and when traffic clears,
    speeds-up to 60 km/hr for the remaining 30 km of the journey. What
    is the average speed?

        >>> harmonic_mean([40, 60], weights=[5, 30])
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    If ``data`` is empty, or any element is less than zero,
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    The *interval* is width of each bin.

    For example, demographic information may have been summarized into
    consecutive ten-year age groups with each group being represented
    by the 5-year midpoints of the intervals:

        >>> demographics = Counter({
        ...    25: 172,   # 20 to 30 years old
        ...    35: 484,   # 30 to 40 years old
        ...    45: 387,   # 40 to 50 years old
        ...    55:  22,   # 50 to 60 years old
        ...    65:   6,   # 60 to 70 years old
        ... })

    The 50th percentile (median) is the 536th person out of the 1071
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    The regular median() function would assume that everyone in the
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        >>> data = list(demographics.elements())
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        35
        >>> round(median_grouped(data, interval=10), 1)
        37.5

    The caller is responsible for making sure the data points are separated
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        3

    This also works with nominal (non-numeric) data:

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        'red'

    If there are multiple modes with same frequency, return the first one
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    Use this function when your data is a sample from a population. To
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    Examples:

    >>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
    >>> variance(data)
    1.3720238095238095

    If you have already calculated the mean of your data, you can pass it as
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    >>> m = mean(data)
    >>> variance(data, m)
    1.3720238095238095

    This function does not check that ``xbar`` is actually the mean of
    ``data``. Giving arbitrary values for ``xbar`` may lead to invalid or
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    Decimals and Fractions are supported:

    >>> from decimal import Decimal as D
    >>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
    Decimal('31.01875')

    >>> from fractions import Fraction as F
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    Use this function to calculate the variance from the entire population.
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    >>> y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
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