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SciPy Statistical Functions

Last Updated : 23 Jul, 2025

SciPy provides a comprehensive set of statistical functions in its scipy.stats module. These tools are important for performing descriptive statistics, statistical testing, probability distributions and random variable operations in scientific and data analysis workflows.

The following table summarizes key statistical functions in SciPy

Function

Description

Mean()

Calculates the average of a dataset by summing all values and dividing by the number of values.

Mode()

Finds the most frequent value(s) in a dataset.

Median()

Identifies the middle value in a sorted dataset.

standard deviation

Measures the spread of data points around the mean

harmonic mean

Calculates the reciprocal of the average of the reciprocals, useful for rates.

variance

A measure of spread, calculated as the average squared deviation from the mean.

standard error

The standard deviation of a sampling distribution, indicating variability.

percentile

A value below which a given percentage of observations fall

skewness

Measures the asymmetry of a distribution

log-logistic distribution

Models survival data and is used in reliability analysis.

Student’s t Distribution

Estimates population parameters when the sample size is small..

kurtosis (Fisher or Pearson)

Measures the "tailedness" of a distribution.

Z-score

Measures how many standard deviations a data point is from the mean.

coefficient of variation

Ratio of the standard deviation to the mean, used to measure variability.

cumulative frequency

Shows the running total of frequencies in a dataset.

Continuous Random Variable

A random variable that can take any value within a range (e.g., height, weight, temperature).

gamma continuous random variable

Used to model waiting times or life durations.

exponential continuous random variable

Models time between events in a Poisson process.

generalized exponential continuous random variable

Flexible for modeling data with additional shape parameters.

alpha continuous random variable

Often related to the shape parameter in various probability distributions.

Erlang continuous random variable

A special case of the Gamma distribution, used in queuing theory.

chi continuous random variable

Used in hypothesis testing, particularly the Chi-squared test.

Uniform continuous random variable

All outcomes within a range are equally likely.

Half-logistic continuous random variable

A variant of the logistic distribution, limited to positive values.

arcsine continuous random variable

Models the arcsine of a variable, often used for angle-related data.

Half-Cauchy continuous random variable

Similar to Cauchy but restricted to positive values, often used in Bayesian statistics.

cosine continuous random variable

Based on the cosine function, used in circular data applications.

Frechet left ( Weibull maximum)

Models the maximum values in a dataset, like the largest daily rainfall.

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