FM / python3.6

/snap/core18/2999/usr/lib/python3.6

Name	Size	Mode	Actions
asyncio/	-	0755	rm
collections/	-	0755	rm
concurrent/	-	0755	rm
ctypes/	-	0755	rm
curses/	-	0755	rm
dbm/	-	0755	rm
distutils/	-	0755	rm
email/	-	0755	rm
encodings/	-	0755	rm
html/	-	0755	rm
http/	-	0755	rm
importlib/	-	0755	rm
json/	-	0755	rm
lib-dynload/	-	0755	rm
lib2to3/	-	0755	rm
logging/	-	0755	rm
multiprocessing/	-	0755	rm
pydoc_data/	-	0755	rm
sqlite3/	-	0755	rm
test/	-	0755	rm
unittest/	-	0755	rm
urllib/	-	0755	rm
venv/	-	0755	rm
wsgiref/	-	0755	rm
xml/	-	0755	rm
xmlrpc/	-	0755	rm
__pycache__/	-	0755	rm
abc.py	8727	0644	edit dl rm
aifc.py	32454	0644	edit dl rm
antigravity.py	477	0644	edit dl rm
argparse.py	90568	0644	edit dl rm
ast.py	12166	0644	edit dl rm
asynchat.py	11328	0644	edit dl rm
asyncore.py	20159	0644	edit dl rm
base64.py	20378	0755	edit dl rm
bdb.py	23556	0644	edit dl rm
binhex.py	13954	0644	edit dl rm
bisect.py	2595	0644	edit dl rm
bz2.py	12478	0644	edit dl rm
calendar.py	23213	0644	edit dl rm
cgi.py	36791	0755	edit dl rm
cgitb.py	12018	0644	edit dl rm
chunk.py	5425	0644	edit dl rm
cmd.py	14860	0644	edit dl rm
code.py	10614	0644	edit dl rm
codecs.py	36276	0644	edit dl rm
codeop.py	5994	0644	edit dl rm
colorsys.py	4064	0644	edit dl rm
compileall.py	12125	0644	edit dl rm
configparser.py	53592	0644	edit dl rm
contextlib.py	13162	0644	edit dl rm
copy.py	8815	0644	edit dl rm
copyreg.py	7007	0644	edit dl rm
cProfile.py	5370	0755	edit dl rm
crypt.py	1864	0644	edit dl rm
csv.py	16180	0644	edit dl rm
datetime.py	82034	0644	edit dl rm
decimal.py	320	0644	edit dl rm
difflib.py	84377	0644	edit dl rm
dis.py	18132	0644	edit dl rm
doctest.py	104391	0644	edit dl rm
dummy_threading.py	2815	0644	edit dl rm
enum.py	33606	0644	edit dl rm
filecmp.py	9830	0644	edit dl rm
fileinput.py	14471	0644	edit dl rm
fnmatch.py	3166	0644	edit dl rm
formatter.py	15143	0644	edit dl rm
fractions.py	23639	0644	edit dl rm
ftplib.py	35617	0644	edit dl rm
functools.py	31346	0644	edit dl rm
genericpath.py	4756	0644	edit dl rm
getopt.py	7489	0644	edit dl rm
getpass.py	5994	0644	edit dl rm
gettext.py	21957	0644	edit dl rm
glob.py	5638	0644	edit dl rm
gzip.py	20334	0644	edit dl rm
hashlib.py	9533	0644	edit dl rm
heapq.py	22929	0644	edit dl rm
hmac.py	5057	0644	edit dl rm
imaplib.py	53295	0644	edit dl rm
imghdr.py	3795	0644	edit dl rm
imp.py	10669	0644	edit dl rm
inspect.py	116958	0644	edit dl rm
io.py	3517	0644	edit dl rm
ipaddress.py	74563	0644	edit dl rm
keyword.py	2209	0755	edit dl rm
LICENSE.txt	12769	0644	edit dl rm
linecache.py	5312	0644	edit dl rm
locale.py	77304	0644	edit dl rm
lzma.py	12983	0644	edit dl rm
macpath.py	5971	0644	edit dl rm
macurl2path.py	2732	0644	edit dl rm
mailbox.py	78624	0644	edit dl rm
mailcap.py	9067	0644	edit dl rm
mimetypes.py	21042	0644	edit dl rm
modulefinder.py	23027	0644	edit dl rm
netrc.py	5684	0644	edit dl rm
nntplib.py	43078	0644	edit dl rm
ntpath.py	21174	0644	edit dl rm
nturl2path.py	2444	0644	edit dl rm
numbers.py	10243	0644	edit dl rm
opcode.py	5822	0644	edit dl rm
operator.py	10863	0644	edit dl rm
optparse.py	60371	0644	edit dl rm
os.py	37526	0644	edit dl rm
pathlib.py	48982	0644	edit dl rm
pdb.py	61310	0755	edit dl rm
pickle.py	55691	0644	edit dl rm
pickletools.py	91775	0644	edit dl rm
pipes.py	8916	0644	edit dl rm
pkgutil.py	21315	0644	edit dl rm
platform.py	48198	0755	edit dl rm
plistlib.py	32787	0644	edit dl rm
poplib.py	14964	0644	edit dl rm
posixpath.py	15645	0644	edit dl rm
pprint.py	20860	0644	edit dl rm
profile.py	22019	0755	edit dl rm
pstats.py	26564	0644	edit dl rm
pty.py	4763	0644	edit dl rm
pyclbr.py	13558	0644	edit dl rm
pydoc.py	103818	0755	edit dl rm
py_compile.py	7181	0644	edit dl rm
queue.py	8780	0644	edit dl rm
quopri.py	7252	0755	edit dl rm
random.py	27442	0644	edit dl rm
re.py	15552	0644	edit dl rm
reprlib.py	5336	0644	edit dl rm
rlcompleter.py	7097	0644	edit dl rm
runpy.py	11959	0644	edit dl rm
sched.py	6511	0644	edit dl rm
secrets.py	2038	0644	edit dl rm
selectors.py	19438	0644	edit dl rm
shelve.py	8515	0644	edit dl rm
shlex.py	12956	0644	edit dl rm
shutil.py	40540	0644	edit dl rm
signal.py	2123	0644	edit dl rm
site.py	21766	0644	edit dl rm
sitecustomize.py	-	0	edit dl rm
smtpd.py	34709	0755	edit dl rm
smtplib.py	44208	0755	edit dl rm
sndhdr.py	7088	0644	edit dl rm
socket.py	27443	0644	edit dl rm
socketserver.py	27010	0644	edit dl rm
sre_compile.py	19338	0644	edit dl rm
sre_constants.py	6821	0644	edit dl rm
sre_parse.py	36536	0644	edit dl rm
ssl.py	46400	0644	edit dl rm
stat.py	5038	0644	edit dl rm
statistics.py	20673	0644	edit dl rm
string.py	11795	0644	edit dl rm
stringprep.py	12917	0644	edit dl rm
struct.py	257	0644	edit dl rm
subprocess.py	62339	0644	edit dl rm
sunau.py	18095	0644	edit dl rm
symbol.py	2109	0755	edit dl rm
symtable.py	7277	0644	edit dl rm
sysconfig.py	25057	0644	edit dl rm
tabnanny.py	11401	0755	edit dl rm
tarfile.py	94969	0755	edit dl rm
telnetlib.py	23136	0644	edit dl rm
tempfile.py	31867	0644	edit dl rm
textwrap.py	19558	0644	edit dl rm
this.py	1003	0644	edit dl rm
threading.py	49029	0644	edit dl rm
timeit.py	13332	0755	edit dl rm
token.py	3075	0644	edit dl rm
tokenize.py	29496	0644	edit dl rm
trace.py	28723	0755	edit dl rm
traceback.py	23458	0644	edit dl rm
tracemalloc.py	16658	0644	edit dl rm
tty.py	879	0644	edit dl rm
turtle.py	143620	0644	edit dl rm
types.py	8870	0644	edit dl rm
typing.py	80274	0644	edit dl rm
uu.py	6753	0755	edit dl rm
uuid.py	23971	0644	edit dl rm
warnings.py	18488	0644	edit dl rm
wave.py	17709	0644	edit dl rm
weakref.py	20466	0644	edit dl rm
webbrowser.py	21757	0755	edit dl rm
xdrlib.py	5913	0644	edit dl rm
zipapp.py	7157	0644	edit dl rm
zipfile.py	78184	0644	edit dl rm
_bootlocale.py	1301	0644	edit dl rm
_collections_abc.py	26392	0644	edit dl rm
_compat_pickle.py	8749	0644	edit dl rm
_compression.py	5340	0644	edit dl rm
_dummy_thread.py	5118	0644	edit dl rm
_markupbase.py	14598	0644	edit dl rm
_osx_support.py	19119	0644	edit dl rm
_pydecimal.py	230228	0644	edit dl rm
_pyio.py	88097	0644	edit dl rm
_sitebuiltins.py	3115	0644	edit dl rm
_strptime.py	24747	0644	edit dl rm
_sysconfigdata_m_linux_x86_64-linux-gnu.py	22325	0644	edit dl rm
_threading_local.py	7214	0644	edit dl rm
_weakrefset.py	5705	0644	edit dl rm
__future__.py	4841	0644	edit dl rm
__phello__.foo.py	64	0644	edit dl rm

Edit: /snap/core18/2999/usr/lib/python3.6/statistics.py (20673B)

"""
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.

"""

__all__ = [ 'StatisticsError',
            'pstdev', 'pvariance', 'stdev', 'variance',
            'median',  'median_low', 'median_high', 'median_grouped',
            'mean', 'mode', 'harmonic_mean',
          ]

import collections
import decimal
import math
import numbers

from fractions import Fraction
from decimal import Decimal
from itertools import groupby, chain
from bisect import bisect_left, bisect_right

# === Exceptions ===

class StatisticsError(ValueError):
    pass

# === Private utilities ===

def _sum(data, start=0):
    """_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.
    """
    count = 0
    n, d = _exact_ratio(start)
    partials = {d: n}
    partials_get = partials.get
    T = _coerce(int, type(start))
    for typ, values in groupby(data, type):
        T = _coerce(T, typ)  # or raise TypeError
        for n,d in map(_exact_ratio, values):
            count += 1
            partials[d] = partials_get(d, 0) + n
    if None in partials:
        # The sum will be a NAN or INF. We can ignore all the finite
        # partials, and just look at this special one.
        total = partials[None]
        assert not _isfinite(total)
    else:
        # Sum all the partial sums using builtin sum.
        # FIXME is this faster if we sum them in order of the denominator?
        total = sum(Fraction(n, d) for d, n in sorted(partials.items()))
    return (T, total, count)

def _isfinite(x):
    try:
        return x.is_finite()  # Likely a Decimal.
    except AttributeError:
        return math.isfinite(x)  # Coerces to float first.

def _coerce(T, S):
    """Coerce 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.
    """
    # See http://bugs.python.org/issue24068.
    assert T is not bool, "initial type T is bool"
    # If the types are the same, no need to coerce anything. Put this
    # first, so that the usual case (no coercion needed) happens as soon
    # as possible.
    if T is S:  return T
    # Mixed int & other coerce to the other type.
    if S is int or S is bool:  return T
    if T is int:  return S
    # If one is a (strict) subclass of the other, coerce to the subclass.
    if issubclass(S, T):  return S
    if issubclass(T, S):  return T
    # Ints coerce to the other type.
    if issubclass(T, int):  return S
    if issubclass(S, int):  return T
    # Mixed fraction & float coerces to float (or float subclass).
    if issubclass(T, Fraction) and issubclass(S, float):
        return S
    if issubclass(T, float) and issubclass(S, Fraction):
        return T
    # Any other combination is disallowed.
    msg = "don't know how to coerce %s and %s"
    raise TypeError(msg % (T.__name__, S.__name__))

def _exact_ratio(x):
    """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.
    """
    try:
        # Optimise the common case of floats. We expect that the most often
        # used numeric type will be builtin floats, so try to make this as
        # fast as possible.
        if type(x) is float or type(x) is Decimal:
            return x.as_integer_ratio()
        try:
            # x may be an int, Fraction, or Integral ABC.
            return (x.numerator, x.denominator)
        except AttributeError:
            try:
                # x may be a float or Decimal subclass.
                return x.as_integer_ratio()
            except AttributeError:
                # Just give up?
                pass
    except (OverflowError, ValueError):
        # float NAN or INF.
        assert not _isfinite(x)
        return (x, None)
    msg = "can't convert type '{}' to numerator/denominator"
    raise TypeError(msg.format(type(x).__name__))

def _convert(value, T):
    """Convert value to given numeric type T."""
    if type(value) is T:
        # This covers the cases where T is Fraction, or where value is
        # a NAN or INF (Decimal or float).
        return value
    if issubclass(T, int) and value.denominator != 1:
        T = float
    try:
        # FIXME: what do we do if this overflows?
        return T(value)
    except TypeError:
        if issubclass(T, Decimal):
            return T(value.numerator)/T(value.denominator)
        else:
            raise

def _counts(data):
    # Generate a table of sorted (value, frequency) pairs.
    table = collections.Counter(iter(data)).most_common()
    if not table:
        return table
    # Extract the values with the highest frequency.
    maxfreq = table[0][1]
    for i in range(1, len(table)):
        if table[i][1] != maxfreq:
            table = table[:i]
            break
    return table

def _find_lteq(a, x):
    'Locate the leftmost value exactly equal to x'
    i = bisect_left(a, x)
    if i != len(a) and a[i] == x:
        return i
    raise ValueError

def _find_rteq(a, l, x):
    'Locate the rightmost value exactly equal to x'
    i = bisect_right(a, x, lo=l)
    if i != (len(a)+1) and a[i-1] == x:
        return i-1
    raise ValueError

def _fail_neg(values, errmsg='negative value'):
    """Iterate over values, failing if any are less than zero."""
    for x in values:
        if x < 0:
            raise StatisticsError(errmsg)
        yield x

# === Measures of central tendency (averages) ===

def mean(data):
    """Return 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.
    """
    if iter(data) is data:
        data = list(data)
    n = len(data)
    if n < 1:
        raise StatisticsError('mean requires at least one data point')
    T, total, count = _sum(data)
    assert count == n
    return _convert(total/n, T)

def harmonic_mean(data):
    """Return 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``.
    """
    # For a justification for using harmonic mean for P/E ratios, see
    # http://fixthepitch.pellucid.com/comps-analysis-the-missing-harmony-of-summary-statistics/
    # http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2621087
    if iter(data) is data:
        data = list(data)
    errmsg = 'harmonic mean does not support negative values'
    n = len(data)
    if n < 1:
        raise StatisticsError('harmonic_mean requires at least one data point')
    elif n == 1:
        x = data[0]
        if isinstance(x, (numbers.Real, Decimal)):
            if x < 0:
                raise StatisticsError(errmsg)
            return x
        else:
            raise TypeError('unsupported type')
    try:
        T, total, count = _sum(1/x for x in _fail_neg(data, errmsg))
    except ZeroDivisionError:
        return 0
    assert count == n
    return _convert(n/total, T)

# FIXME: investigate ways to calculate medians without sorting? Quickselect?
def median(data):
    """Return 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

"""
    data = sorted(data)
    n = len(data)
    if n == 0:
        raise StatisticsError("no median for empty data")
    if n%2 == 1:
        return data[n//2]
    else:
        i = n//2
        return (data[i - 1] + data[i])/2

def median_low(data):
    """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

"""
    data = sorted(data)
    n = len(data)
    if n == 0:
        raise StatisticsError("no median for empty data")
    if n%2 == 1:
        return data[n//2]
    else:
        return data[n//2 - 1]

def median_high(data):
    """Return 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

"""
    data = sorted(data)
    n = len(data)
    if n == 0:
        raise StatisticsError("no median for empty data")
    return data[n//2]

def median_grouped(data, interval=1):
    """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.
    """
    data = sorted(data)
    n = len(data)
    if n == 0:
        raise StatisticsError("no median for empty data")
    elif n == 1:
        return data[0]
    # Find the value at the midpoint. Remember this corresponds to the
    # centre of the class interval.
    x = data[n//2]
    for obj in (x, interval):
        if isinstance(obj, (str, bytes)):
            raise TypeError('expected number but got %r' % obj)
    try:
        L = x - interval/2  # The lower limit of the median interval.
    except TypeError:
        # Mixed type. For now we just coerce to float.
        L = float(x) - float(interval)/2

# Uses bisection search to search for x in data with log(n) time complexity
    # Find the position of leftmost occurrence of x in data
    l1 = _find_lteq(data, x)
    # Find the position of rightmost occurrence of x in data[l1...len(data)]
    # Assuming always l1 <= l2
    l2 = _find_rteq(data, l1, x)
    cf = l1
    f = l2 - l1 + 1
    return L + interval*(n/2 - cf)/f

def mode(data):
    """Return 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.
    """
    # Generate a table of sorted (value, frequency) pairs.
    table = _counts(data)
    if len(table) == 1:
        return table[0][0]
    elif table:
        raise StatisticsError(
                'no unique mode; found %d equally common values' % len(table)
                )
    else:
        raise StatisticsError('no mode for empty data')

# === Measures of spread ===

# See http://mathworld.wolfram.com/Variance.html
#     http://mathworld.wolfram.com/SampleVariance.html
#     http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
#
# Under no circumstances use the so-called "computational formula for
# variance", as that is only suitable for hand calculations with a small
# amount of low-precision data. It has terrible numeric properties.
#
# See a comparison of three computational methods here:
# http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/

def _ss(data, c=None):
    """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.
    """
    if c is None:
        c = mean(data)
    T, total, count = _sum((x-c)**2 for x in data)
    # The following sum should mathematically equal zero, but due to rounding
    # error may not.
    U, total2, count2 = _sum((x-c) for x in data)
    assert T == U and count == count2
    total -=  total2**2/len(data)
    assert not total < 0, 'negative sum of square deviations: %f' % total
    return (T, total)

def variance(data, xbar=None):
    """Return 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)

"""
    if iter(data) is data:
        data = list(data)
    n = len(data)
    if n < 2:
        raise StatisticsError('variance requires at least two data points')
    T, ss = _ss(data, xbar)
    return _convert(ss/(n-1), T)

def pvariance(data, mu=None):
    """Return 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)

"""
    if iter(data) is data:
        data = list(data)
    n = len(data)
    if n < 1:
        raise StatisticsError('pvariance requires at least one data point')
    T, ss = _ss(data, mu)
    return _convert(ss/n, T)

def stdev(data, xbar=None):
    """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

"""
    var = variance(data, xbar)
    try:
        return var.sqrt()
    except AttributeError:
        return math.sqrt(var)

def pstdev(data, mu=None):
    """Return 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

"""
    var = pvariance(data, mu)
    try:
        return var.sqrt()
    except AttributeError:
        return math.sqrt(var)

cmd: