Basic statistics module.
This module provides functions for calculating statistics of data, including
averages, variance, and standard deviation.
Calculating averages
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Function Description
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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.
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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
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Function Description
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pvariance Population variance of data.
variance Sample variance of data.
pstdev Population standard deviation of data.
stdev Sample standard deviation of data.
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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
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Function Description
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covariance Sample covariance for two variables.
correlation Pearson's correlation coefficient for two variables.
linear_regression Intercept and slope for simple linear regression.
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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
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A single exception is defined: StatisticsError is a subclass of ValueError.© Python Software Foundation. PSF License Version 2 · Official docs ↗