def stdev(data, m=None):
"""stdev(iterable_of_numbers [, m]) -> standard deviation of numbers
stdev(iterable_of_rows [, m]) -> standard deviation of columns
Returns the sample standard deviation (with N-1 degrees of freedom)
of the given numbers or columns. The standard deviation is the square
root of the variance.
Optional argument ``m`` has the same meaning as for ``variance``.
>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) #doctest: +ELLIPSIS
1.08108741552...
>>> data = [[0, 1, 2],
... [1, 1, 3],
... [1, 2, 5],
... [2, 4, 6]]
...
>>> stdev(data) #doctest: +ELLIPSIS
[0.816496580927..., 1.41421356237..., 1.82574185835...]
Note that although ``variance`` is an unbiased estimate for the
population variance, ``stdev`` itself is *not* unbiased.
"""
svar = variance(data, m)
return v.sqrt(svar)
def quadratic_mean(data):
"""quadratic_mean(iterable_of_numbers) -> quadratic mean of numbers
quadratic_mean(iterable_of_rows) -> quadratic means of columns
Return the quadratic mean of the given numbers or columns.
>>> quadratic_mean([2, 2, 4, 5])
3.5
The quadratic mean, or RMS (Root Mean Square), is the square root of the
arithmetic mean of the squares of the data. It is a type of average
best used to get an average absolute magnitude when quantities vary from
positive to negative:
>>> quadratic_mean([-3, -2, 0, 2, 3])
2.280350850198276
When passed an iterable of sequences, each inner sequence represents a
row of data, and ``quadratic_mean`` operates on each column. All rows
must have the same number of columns, or ValueError is raised.
>>> data = [[0, 1, 2, 4],
... [1, 2, 4, 6],
... [2, 4, 6, 6]]
...
>>> quadratic_mean(data) #doctest: +ELLIPSIS
[1.29099..., 2.64575..., 4.3204..., 5.41602...]
"""
count, total = stats._len_sum(v.sqr(x) for x in data)
if not count:
raise stats.StatsError(
'quadratic mean of empty sequence is not defined')
return v.sqrt(v.div(total, count))
def pstdev(data, m=None):
"""pstdev(iterable_of_numbers [, m]) -> population std dev of numbers
pstdev(iterable_of_rows [, m]) -> population std dev of columns
Returns the population standard deviation (with N degrees of freedom)
of the given numbers or columns. The standard deviation is the square
root of the variance.
Optional argument ``m`` has the same meaning as for ``pvariance``.
>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75]) #doctest: +ELLIPSIS
0.986893273527...
>>> data = [[0, 1, 2],
... [1, 1, 3],
... [1, 2, 5],
... [2, 4, 6]]
...
>>> pstdev(data) #doctest: +ELLIPSIS
[0.707106781186..., 1.22474487139..., 1.58113883008...]
"""
pvar = pvariance(data, m)
return v.sqrt(pvar)
