Python’s built-in statistics module provides straightforward tools for summarizing data: averages and medians for central location, variance and standard deviation for spread, and quantiles for cut points. Here are ten useful functions, grouped by purpose—not a complete list. Python 3.14.8 documents additional functions, including covariance, correlation, and linear regression.
Before choosing a function
First decide what your data represents. A sample is a subset used to estimate a larger group; a population is the entire group you want to describe. That distinction determines which variance and standard-deviation functions to use.
Most functions in the module support int, float, Decimal, and Fraction values. Avoid mixing numeric types in one dataset: behavior for mixed-type collections is undefined and implementation-dependent. Remove NaNs before calling functions that sort values or count occurrences, such as median(), mode(), and quantiles().
The examples use the official Python 3.14.8 statistics documentation as their reference. geometric_mean() and quantiles() were added in Python 3.8; weighted harmonic_mean() was added in Python 3.10. In Python 3.13, quantiles() changed to accept a dataset containing a single data point.
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Central location: where is the center?
1. mean(): arithmetic average
mean() adds the values and divides by their count. It works with a sequence or iterable, and raises StatisticsError for empty input.
from statistics import mean
scores = [72, 81, 86, 91]
print(mean(scores)) # 82.5The arithmetic mean is useful when every observation should contribute proportionally, but an extreme value can pull it away from what is typical. For example, a few unusually high incomes can make a group’s mean income much higher than most individuals’ incomes.
For exact arithmetic, the function can preserve supported numeric types such as Decimal and Fraction:
from fractions import Fraction
from statistics import mean
print(mean([Fraction(1, 3), Fraction(2, 3)])) # Fraction(1, 2)2. median(): middle value, or midpoint of the two middle values
median() sorts the data and returns the middle value. When the dataset has an even number of values, it returns the mean of the two middle values; that result need not be an observed value. Because extreme values do not pull it as strongly as they pull the mean, the median can better represent a skewed dataset.
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from statistics import median
print(median([1, 3, 4, 100])) # 3.5For the same sorted values, median_low() and median_high() return the lower or higher middle observation instead. Those are useful when the result must be an actual data point, including for suitable ordinal data such as ranked categories.
3. mode(): one most-common value
mode() returns the most frequently occurring value. It can work with nominal data—categories without a numeric scale—such as color names. If values tie for highest frequency, it returns the first tied value encountered in the input.
from statistics import mode
print(mode(["blue", "red", "blue", "red", "green"])) # blue4. multimode(): every most-common value
Use multimode() when you need all values tied for the highest frequency. It returns them in encounter order, so the example below returns both colors.
from statistics import multimode
print(multimode(["blue", "red", "blue", "red", "green"])) # ['blue', 'red']Specialized averages: when values are rates or multiply together
5. geometric_mean(): multiplicative average
The geometric mean is useful for values that combine multiplicatively, such as growth factors across periods. Unlike the arithmetic mean, it does not average by simple addition. Python converts inputs to floats; the function rejects empty data and any value that is zero or negative.
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from statistics import geometric_mean
print(geometric_mean([1.1, 1.21]))Use it only when the data and question make a multiplicative average appropriate; it is not a drop-in replacement for the arithmetic mean.
6. harmonic_mean(): average for rates and ratios
The harmonic mean is often appropriate for averaging rates or ratios. The Python documentation gives speed as an example: averaging speeds over equal distances is different from taking their arithmetic mean.
from statistics import harmonic_mean
print(harmonic_mean([40, 60]))Python also supports weighted harmonic means; that capability was added in Python 3.10. Supply weights when observations represent different amounts of the quantity being averaged, and make sure the weights match the data in length and meaning.
Spread: how much do observations vary?
7. variance(): sample variance
Use variance() when your data is a sample and you want to estimate variance in a larger population. It uses N − 1 degrees of freedom, where N is the sample size, and requires at least two data points.
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from statistics import variance
measurements = [2, 4, 6, 8]
print(variance(measurements))An optional xbar argument lets you supply the sample mean, but Python does not check that your value is correct. A mistaken xbar can therefore produce a misleading result.
8. pvariance(): population variance
Use pvariance() when your dataset contains the whole population of interest, rather than a sample. It divides by N, not N − 1.
from statistics import pvariance
entire_group = [2, 4, 6, 8]
print(pvariance(entire_group))Do not choose between variance() and pvariance() based on which result looks preferable. Choose according to whether the observations are a sample or the full population.
9. stdev(): sample standard deviation
stdev() is the square root of the sample variance. Like variance(), it treats the data as a sample and requires at least two values. Because it is expressed in the same units as the original measurements, it is often easier to interpret than variance.
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from statistics import stdev
print(stdev([2, 4, 6, 8]))10. pstdev(): population standard deviation
pstdev() is the square root of the population variance. Use it for a complete population, not a sample.
from statistics import pstdev
print(pstdev([2, 4, 6, 8]))Bonus: divide data into quantiles
quantiles() is an additional useful function, not included in the ten above. It returns cut points that divide ordered data into a chosen number of intervals. By default, n=4 returns quartile cut points, using the exclusive method.
from statistics import quantiles
values = [1, 2, 3, 4, 5, 6, 7, 8]
print(quantiles(values, n=4, method="exclusive"))The method matters: exclusive and inclusive can produce different cut points. The inclusive method treats the observed minimum and maximum as the 0th and 100th percentiles. State which method you use when reporting results rather than treating quantile cut points as method-independent.
Where the built-in module fits
The statistics module is suitable for basic statistical calculations directly in Python. The Python documentation says: “The module is not intended to be a competitor to third-party libraries such as NumPy, SciPy, or proprietary full-featured statistics packages aimed at professional statisticians such as Minitab, SAS and Matlab.”
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