Python Random Sampling and Statistics

The essentials

Quick reference

One focused task per row. Jump to the related section for complete, working examples.

Use	Syntax	Examples
Create a local generator	`rng = random.Random(seed)`	View examples
Capture generator state	`state = rng.getstate()`	View examples
Restore generator state	`rng.setstate(state)`	View examples
Draw from range semantics	`value = rng.randrange(start, stop, step)`	View examples
Choose one element	`item = rng.choice(population)`	View examples
Sample without replacement	`items = rng.sample(population, k=3)`	View examples
Sample by relative weight	`draws = rng.choices(population, weights=weights, k=100)`	View examples
Draw a uniform float	`value = rng.uniform(low, high)`	View examples
Draw from a normal model	`value = rng.normalvariate(mu, sigma)`	View examples
Generate random bytes	`token = secrets.token_bytes(32)`	View examples
Generate a URL-safe token	`token = secrets.token_urlsafe(32)`	View examples
Choose securely	`character = secrets.choice(alphabet)`	View examples
Compute an arithmetic mean	`center = statistics.mean(values)`	View examples
Compute a median	`center = statistics.median(values)`	View examples
Find all most-common values	`modes = statistics.multimode(values)`	View examples
Estimate sample spread	`spread = statistics.stdev(sample)`	View examples
Measure population spread	`spread = statistics.pstdev(population)`	View examples
Compute linear correlation	`coefficient = statistics.correlation(xs, ys)`	View examples
Estimate sample quartiles	`cuts = statistics.quantiles(values, n=4, method='exclusive')`	View examples
Summarize observed endpoints	`cuts = statistics.quantiles(values, n=4, method='inclusive')`	View examples

The random module provides deterministic pseudo-random generators for simulation, while secrets uses operating-system entropy for credentials and security tokens. The statistics module supplies transparent descriptive tools, but correct results still depend on sampling design, missing-data policy, numeric types, and the meaning of the population being summarized.

Step by step

Detailed examples

Own generator state for reproducible simulations

Create a dedicated random.Random instance instead of mutating the module-global generator in libraries. A seed recreates a pseudo-random state for debugging but is not secret entropy. Record the algorithm/runtime context when long-term replay matters; getstate and setstate can checkpoint a run but their serialized representation is Python-specific.

Replay a local generator state

import random

rng = random.Random(23)
state = rng.getstate()
first = [rng.randrange(10) for _ in range(4)]
rng.setstate(state)
second = [rng.randrange(10) for _ in range(4)]
print(first)
print(first == second)

Output

[4, 1, 0, 9]
True

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Select discrete outcomes without off-by-one errors

randrange follows range semantics and excludes stop; randint(a, b) includes both endpoints. choice selects one element, choices samples with replacement, and sample selects unique positions without replacement. Sampling a population containing repeated values treats each position as a possible selection unless counts is used to express multiplicities.

Sample without replacement reproducibly

import random

rng = random.Random(7)
sample = rng.sample(["a", "b", "c", "d", "e"], k=3)
print(sample)
print(len(set(sample)) == 3)

Output

['c', 'b', 'd']
True

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Model weights and distributions explicitly

choices accepts relative weights or cumulative weights and samples with replacement. Distribution functions such as uniform, gauss, normalvariate, expovariate, and triangular encode specific mathematical models; validate parameter units and domain assumptions. Floating-point endpoints and tails need policy-driven bounds rather than equality tests.

Use zero weights to make a deterministic choice

import random

rng = random.Random(1)
draws = rng.choices(["disabled", "enabled"], weights=[0, 5], k=4)
print(draws)

Output

['enabled', 'enabled', 'enabled', 'enabled']

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Use secrets for security-sensitive choices

random is predictable from state and must not generate passwords, reset links, session identifiers, salts, or cryptographic nonces. secrets delegates to the operating system's strongest available source. Token output is intentionally nondeterministic; validate entropy requirements in bytes or bits rather than assuming a displayed character count provides equivalent entropy.

Validate a secure token without fixing its value

import secrets

token = secrets.token_bytes(16)
print(type(token).__name__)
print(len(token))
print(len(token) * 8)

Output

bytes
16
128

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Choose a center that matches the data

mean uses every value and is sensitive to outliers; median is robust to extremes; mode and multimode describe frequency. fmean converts input to float and is usually faster, while mean preserves supported numeric types where possible. Empty data and mixed incompatible numeric types need explicit handling rather than fallback zeroes.

Compare mean and median under an outlier

import statistics

values = [2, 3, 3, 4, 100]
print(statistics.mean(values))
print(statistics.median(values))
print(statistics.multimode(values))

Output

22.4
3
[3]

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Distinguish samples from populations

pstdev and pvariance divide by population size; stdev and variance apply Bessel's correction for sample estimates and require at least two observations. covariance and correlation describe paired observations and do not establish causation. NaN values can break ordering-based functions, so filter or reject them according to a documented missing-data policy.

Compare sample and population variance

import statistics

values = [1, 2, 3]
print(statistics.pvariance(values))
print(statistics.variance(values))
print(statistics.correlation(values, [2, 4, 6]))

Output

0.6666666666666666
1
1.0

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Report distributions with explicit conventions

quantiles divides data into equal-probability intervals using exclusive or inclusive conventions. Exclusive is suited to samples from a larger population; inclusive treats the observed minimum and maximum as population endpoints. Statistics do not repair selection bias, dependent observations, censoring, or a changing process; preserve raw counts and definitions beside summaries.

Compute inclusive quartiles

import statistics

values = [10, 20, 30, 40, 50]
print(statistics.quantiles(values, n=4, method="inclusive"))
print(min(values), max(values))

Output

[20.0, 30.0, 40.0]
10 50

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Local code tester

Summarize a reproducible sample

Draw a local deterministic sample and report its center and spread without changing global generator state.

Runs in your browser

Python

import random
import statistics

rng = random.Random(11)
sample = rng.sample(range(1, 11), k=5)
print(sample)
print(statistics.median(sample))
print(round(statistics.pstdev(sample), 2))

Output

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Sources and further reading

References

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Quick reference

Detailed examples

Own generator state for reproducible simulations

Select discrete outcomes without off-by-one errors

Model weights and distributions explicitly

Use secrets for security-sensitive choices

Choose a center that matches the data

Distinguish samples from populations

Report distributions with explicit conventions

Summarize a reproducible sample

More Python cheat sheets

Python bytes, bytearray, memoryview, and Binary Data Cheat Sheet

Python Dates, Times, and Time Zones Cheat Sheet

Python Decimal, Fractions, and Numeric Precision Cheat Sheet

References

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