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Mathematical techniques used for mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory


Return the high median of data. If data is empty, StatisticsError is raised. data can be a sequence or iterator.

The high median is always a member of the data set. 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])
>>> median_high([1, 3, 5, 7])

Use the high median when your data are discrete and you prefer the median to be an actual data point rather than interpolated.statistics.median_grouped(datainterval=1)

Return the median of grouped continuous data, calculated as the 50th percentile, using interpolation. If datais empty, StatisticsError is raised. data can be a sequence or iterator.

>>> median_grouped([52, 52, 53, 54])

In the following example, the data are rounded, so that each value represents the midpoint of data classes, e.g. 1 is the midpoint of the class 0.5–1.5, 2 is the midpoint of 1.5–2.5, 3 is the midpoint of 2.5–3.5, etc. With the data given, the middle value falls somewhere in the class 3.5–4.5, and interpolation is used to estimate it:

>>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])

Optional argument interval represents the class interval, and defaults to 1. Changing the class interval naturally will change the interpolation:

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

This function does not check whether the data points are at least interval apart.

CPython implementation detail: Under some circumstances, median_grouped() may coerce data points to floats. This behaviour is likely to change in the future.

See also

  • “Statistics for the Behavioral Sciences”, Frederick J Gravetter and Larry B Wallnau (8th Edition).
  • The SSMEDIAN function in the Gnome Gnumeric spreadsheet, including this discussion.


Return the most common data point from discrete or nominal data. The mode (when it exists) is the most typical value, and is a robust measure of central location.

If data is empty, or if there is not exactly one most common value, StatisticsError is raised.

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])

The mode is unique in that it is the only statistic which also applies to nominal (non-numeric) data:

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


Return the population standard deviation (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])