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Current File : //lib64/python3.6/__pycache__/statistics.cpython-36.pyc
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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.
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.
==================  =============================================

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


Exceptions
----------

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

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harmonic_meanéN)ÚFraction)ÚDecimal)ÚgroupbyÚchain)Úbisect_leftÚbisect_rightc@seZdZdS)rN)Ú__name__Ú
__module__Ú__qualname__©rrú"/usr/lib64/python3.6/statistics.pyrcscCsÄd}t|ƒ\}}||i}|j}ttt|ƒƒ}xRt|tƒD]D\}}	t||ƒ}x0tt|	ƒD]"\}}|d7}||dƒ|||<qVWq8Wd|kr |d}
t|
ƒsºt‚nt	dd„t
|jƒƒDƒƒ}
||
|fS)aC_sum(data [, start]) -> (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.

    If optional argument ``start`` is given, it is added to the total.
    If ``data`` is empty, ``start`` (defaulting to 0) is returned.


    Examples
    --------

    >>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75)
    (<class 'float'>, Fraction(11, 1), 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
    >>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])
    (<class 'fractions.Fraction'>, Fraction(63, 20), 4)

    >>> from decimal import Decimal as D
    >>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]
    >>> _sum(data)
    (<class 'decimal.Decimal'>, Fraction(6963, 10000), 4)

    Mixed types are currently treated as an error, except that int is
    allowed.
    r
éNcss|]\}}t||ƒVqdS)N)r)Ú.0ÚdÚnrrrú	<genexpr>Ÿsz_sum.<locals>.<genexpr>)Ú_exact_ratioÚgetÚ_coerceÚintÚtyperÚmapÚ	_isfiniteÚAssertionErrorÚsumÚsortedÚitems)ÚdataÚstartÚcountrrZpartialsZpartials_getÚTÚtypÚvaluesÚtotalrrrÚ_sumis$
r0cCs(y|jƒStk
r"tj|ƒSXdS)N)Z	is_finiteÚAttributeErrorÚmathZisfinite)Úxrrrr$£sr$cCsÀ|tk	stdƒ‚||kr|S|tks,|tkr0|S|tkr<|St||ƒrJ|St||ƒrX|St|tƒrf|St|tƒrt|St|tƒrŒt|tƒrŒ|St|tƒr¤t|tƒr¤|Sd}t||j|jfƒ‚dS)z½Coerce types T and S to a common type, or raise TypeError.

    Coercion rules are currently an implementation detail. See the CoerceTest
    test class in test_statistics for details.
    zinitial type T is boolz"don't know how to coerce %s and %sN)Úboolr%r!Ú
issubclassrÚfloatÚ	TypeErrorr)r,ÚSÚmsgrrrr ªs*



r cCs¬ydt|ƒtkst|ƒtkr"|jƒSy|j|jfStk
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‚|dfSXd}t|jt|ƒj
ƒƒ‚dS)z¥Return Real number x to exact (numerator, denominator) pair.

    >>> _exact_ratio(0.25)
    (1, 4)

    x is expected to be an int, Fraction, Decimal or float.
    Nz0can't convert type '{}' to numerator/denominator)r"r6rÚas_integer_ratioÚ	numeratorÚdenominatorr1Ú
OverflowErrorÚ
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rcCsjt|ƒ|kr|St|tƒr(|jdkr(t}y||ƒStk
rdt|tƒr^||jƒ||jƒS‚YnXdS)z&Convert value to given numeric type T.rN)r"r5r!r<r6r7rr;)Úvaluer,rrrÚ_convertés
rAcCs`tjt|ƒƒjƒ}|s|S|dd}x4tdt|ƒƒD]"}||d|kr6|d|…}Pq6W|S)Nr
r)ÚcollectionsÚCounterÚiterÚmost_commonÚrangeÚlen)r)ÚtableZmaxfreqÚirrrÚ_countsûsrJcCs.t||ƒ}|t|ƒkr&|||kr&|St‚dS)z,Locate the leftmost value exactly equal to xN)rrGr>)Úar3rIrrrÚ
_find_lteq	s
rLcCs>t|||d}|t|ƒdkr6||d|kr6|dSt‚dS)z-Locate the rightmost value exactly equal to x)ÚlorN)rrGr>)rKÚlr3rIrrrÚ
_find_rteqs rOúnegative valueccs(x"|D]}|dkrt|ƒ‚|VqWdS)z7Iterate over values, failing if any are less than zero.r
N)r)r.Úerrmsgr3rrrÚ	_fail_negs
rRcCsTt|ƒ|krt|ƒ}t|ƒ}|dkr,tdƒ‚t|ƒ\}}}||ksFt‚t|||ƒS)aƒReturn the sample arithmetic mean of data.

    >>> mean([1, 2, 3, 4, 4])
    2.8

    >>> from fractions import Fraction as F
    >>> mean([F(3, 7), F(1, 21), F(5, 3), F(1, 3)])
    Fraction(13, 21)

    >>> from decimal import Decimal as D
    >>> mean([D("0.5"), D("0.75"), D("0.625"), D("0.375")])
    Decimal('0.5625')

    If ``data`` is empty, StatisticsError will be raised.
    rz%mean requires at least one data point)rDÚlistrGrr0r%rA)r)rr,r/r+rrrr
#scCsÀt|ƒ|krt|ƒ}d}t|ƒ}|dkr2tdƒ‚n<|dkrn|d}t|tjtfƒrf|dkrbt|ƒ‚|Stdƒ‚y"t	dd„t
||ƒDƒƒ\}}}Wntk
r¤dSX||ks²t‚t
|||ƒS)aReturn the harmonic mean of data.

    The harmonic mean, sometimes called the subcontrary mean, is the
    reciprocal of the arithmetic mean of the reciprocals of the data,
    and is often appropriate when averaging quantities which are rates
    or ratios, for example speeds. Example:

    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?

    >>> harmonic_mean([2.5, 3, 10])  # For an equal investment portfolio.
    3.6

    Using the arithmetic mean would give an average of about 5.167, which
    is too high.

    If ``data`` is empty, or any element is less than zero,
    ``harmonic_mean`` will raise ``StatisticsError``.
    z.harmonic mean does not support negative valuesrz.harmonic_mean requires at least one data pointr
zunsupported typecss|]}d|VqdS)rNr)rr3rrrrdsz harmonic_mean.<locals>.<genexpr>)rDrSrGrÚ
isinstanceÚnumbersZRealrr7r0rRÚZeroDivisionErrorr%rA)r)rQrr3r,r/r+rrrr=s&
"cCs\t|ƒ}t|ƒ}|dkr tdƒ‚|ddkr8||dS|d}||d||dSdS)aBReturn the median (middle value) of numeric data.

    When the number of data points is odd, return the middle data point.
    When the number of data points is even, the median is interpolated by
    taking the average of the two middle values:

    >>> median([1, 3, 5])
    3
    >>> median([1, 3, 5, 7])
    4.0

    r
zno median for empty dataérN)r'rGr)r)rrIrrrrls
cCsLt|ƒ}t|ƒ}|dkr tdƒ‚|ddkr8||dS||ddSdS)a	Return the low median of numeric data.

    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.

    >>> median_low([1, 3, 5])
    3
    >>> median_low([1, 3, 5, 7])
    3

    r
zno median for empty datarWrN)r'rGr)r)rrrrr„scCs,t|ƒ}t|ƒ}|dkr tdƒ‚||dS)aReturn the high median of data.

    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.

    >>> median_high([1, 3, 5])
    3
    >>> median_high([1, 3, 5, 7])
    5

    r
zno median for empty datarW)r'rGr)r)rrrrršs
rc
Csât|ƒ}t|ƒ}|dkr"tdƒ‚n|dkr2|dS||d}x*||fD]}t|ttfƒrHtd|ƒ‚qHWy||d}Wn(tk
r¢t|ƒt|ƒd}YnXt||ƒ}t	|||ƒ}|}||d}	|||d||	S)a£Return the 50th percentile (median) of grouped continuous data.

    >>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
    3.7
    >>> median_grouped([52, 52, 53, 54])
    52.5

    This calculates the median as the 50th percentile, and should be
    used when your data is continuous and grouped. In the above example,
    the values 1, 2, 3, etc. actually represent the midpoint of classes
    0.5-1.5, 1.5-2.5, 2.5-3.5, etc. The middle value falls somewhere in
    class 3.5-4.5, and interpolation is used to estimate it.

    Optional argument ``interval`` represents the class interval, and
    defaults to 1. Changing the class interval naturally will change the
    interpolated 50th percentile value:

    >>> median_grouped([1, 3, 3, 5, 7], interval=1)
    3.25
    >>> median_grouped([1, 3, 3, 5, 7], interval=2)
    3.5

    This function does not check whether the data points are at least
    ``interval`` apart.
    r
zno median for empty datarrWzexpected number but got %r)
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r)Zintervalrr3ÚobjÚLÚl1Úl2ZcfÚfrrrr	s&

cCsBt|ƒ}t|ƒdkr |ddS|r6tdt|ƒƒ‚ntdƒ‚dS)aäReturn the most common data point from discrete or nominal data.

    ``mode`` assumes discrete data, and returns a single value. This is the
    standard treatment of the mode as commonly taught in schools:

    >>> mode([1, 1, 2, 3, 3, 3, 3, 4])
    3

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

    >>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
    'red'

    If there is not exactly one most common value, ``mode`` will raise
    StatisticsError.
    rr
z.no unique mode; found %d equally common valueszno mode for empty dataN)rJrGr)r)rHrrrräscsŽˆdkrt|ƒ‰t‡fdd„|Dƒƒ\}}}t‡fdd„|Dƒƒ\}}}||krX||ks\t‚||dt|ƒ8}|dks†td|ƒ‚||fS)a;Return sum of square deviations of sequence data.

    If ``c`` is None, the mean is calculated in one pass, and the deviations
    from the mean are calculated in a second pass. Otherwise, deviations are
    calculated from ``c`` as given. Use the second case with care, as it can
    lead to garbage results.
    Nc3s|]}|ˆdVqdS)rWNr)rr3)Úcrrrsz_ss.<locals>.<genexpr>c3s|]}|ˆVqdS)Nr)rr3)r_rrrsrWr
z%negative sum of square deviations: %f)r
r0r%rG)r)r_r,r/r+ÚUZtotal2Zcount2r)r_rÚ_sssracCsLt|ƒ|krt|ƒ}t|ƒ}|dkr,tdƒ‚t||ƒ\}}t||d|ƒS)aÂReturn the sample variance of data.

    data should be an iterable of Real-valued numbers, with at least two
    values. The optional argument xbar, if given, should be the mean of
    the data. If it is missing or None, the mean is automatically calculated.

    Use this function when your data is a sample from a population. To
    calculate the variance from the entire population, see ``pvariance``.

    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
    the optional second argument ``xbar`` to avoid recalculating it:

    >>> 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
    impossible results.

    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
    >>> variance([F(1, 6), F(1, 2), F(5, 3)])
    Fraction(67, 108)

    rWz*variance requires at least two data pointsr)rDrSrGrrarA)r)Úxbarrr,Ússrrrr"s&cCsHt|ƒ|krt|ƒ}t|ƒ}|dkr,tdƒ‚t||ƒ\}}t|||ƒS)aÇReturn the population variance of ``data``.

    data should be an iterable of Real-valued numbers, with at least one
    value. The optional argument mu, if given, should be the mean of
    the data. If it is missing or None, the mean is automatically calculated.

    Use this function to calculate the variance from the entire population.
    To estimate the variance from a sample, the ``variance`` function is
    usually a better choice.

    Examples:

    >>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
    >>> pvariance(data)
    1.25

    If you have already calculated the mean of the data, you can pass it as
    the optional second argument to avoid recalculating it:

    >>> mu = mean(data)
    >>> pvariance(data, mu)
    1.25

    This function does not check that ``mu`` is actually the mean of ``data``.
    Giving arbitrary values for ``mu`` may lead to invalid or impossible
    results.

    Decimals and Fractions are supported:

    >>> from decimal import Decimal as D
    >>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
    Decimal('24.815')

    >>> from fractions import Fraction as F
    >>> pvariance([F(1, 4), F(5, 4), F(1, 2)])
    Fraction(13, 72)

    rz*pvariance requires at least one data point)rDrSrGrrarA)r)Úmurr,rcrrrrQs'cCs2t||ƒ}y|jƒStk
r,tj|ƒSXdS)z´Return the square root of the sample variance.

    See ``variance`` for arguments and other details.

    >>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
    1.0810874155219827

    N)rÚsqrtr1r2)r)rbÚvarrrrrs
	
cCs2t||ƒ}y|jƒStk
r,tj|ƒSXdS)z¹Return the square root of the population variance.

    See ``pvariance`` for arguments and other details.

    >>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
    0.986893273527251

    N)rrer1r2)r)rdrfrrrr‘s
	
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