# Source code for simplestatistics.statistics.harmonic_mean

from .mean import mean
from .sum import sum
[docs]def harmonic_mean(x):
"""
The `harmonic mean`_ is a kind of average that is calculated as
the reciprocal_ of the arithmetic mean of the reciprocals.
It is appropriate when calculating averages of rates_.
.. _`harmonic mean`: https://en.wikipedia.org/wiki/Harmonic_mean
.. _reciprocal: https://en.wikipedia.org/wiki/Multiplicative_inverse
.. _rates: https://en.wikipedia.org/wiki/Rate_(mathematics)
Equation:
.. math::
H = \\frac{n}{\\frac{1}{x_1}+\\frac{1}{x_2}+\\ldots+\\frac{1}{x_n}} =
\\frac{n}{\\sum\\limits_{i=1}^n \\frac{1}{x_i}}
Args:
x: A list or tuple of numerical objects.
Returns:
A numerical object.
Raises:
TypeError: If the user passes something other than list or tuple.
Examples:
>>> harmonic_mean([1, 2, 4])
1.7142857142857142
>>> harmonic_mean(7)
Traceback (most recent call last):
...
TypeError: harmonic_mean() expects a list or a tuple.
"""
if type(x) not in [list, tuple]:
raise TypeError('harmonic_mean() expects a list or a tuple.')
reciprocals = [1 / float(num) for num in x]
# sum_of_reciprocals = sum(reciprocals[:])
return(1 / mean(reciprocals))