The statistics Module

Reviewed & published by Brayan K

The statistics module is Python's built-in toolkit for calculating averages, spread, and quantiles directly on ordinary lists of numbers, with zero external dependencies.

Part of the free Python course at LearnCodingFast — hands-on lessons with examples you run in your browser, plus practice exercises and a quick quiz.

Before you reach for numpy or pandas, this lightweight standard-library module handles the everyday math — means, medians, modes, and standard deviation — in a few clear function calls.

What You'll Learn in This Lesson

• Measures of center: mean, median, and mode
• Measures of spread: variance and standard deviation
• Sample vs population (stdev vs pstdev)
• Splitting data with quantiles
• Faster averages with fmean and geometric_mean
• When to choose statistics over numpy or pandas

1 Measures of Center: mean, median, mode

The three classic "averages" answer different questions. The mean is the arithmetic average, the median is the middle value when sorted, and the mode is the most common value. Each is a single function call:

import statistics as st

data = [12, 15, 15, 18, 22, 30]

print("mean:", st.mean(data))       # mean: 18.666666666666668
print("median:", st.median(data))   # median: 16.5
print("mode:", st.mode(data))       # mode: 15

💡 Why the median matters:

The median ignores extreme outliers. If one billionaire walks into a room, the mean income skyrockets but the median barely moves. For skewed data like incomes or house prices, the median is usually the more honest "typical" value.

import statistics as st

scores = [70, 85, 85, 90, 95, 100]

print("mean:", round(st.mean(scores), 2))
print("median:", st.median(scores))
print("mode:", st.mode(scores))
print("multimode:", st.multimode([1, 1, 2, 2, 3]))

# ✅ Expected output:
# mean: 87.5
# median: 87.5
# mode: 85
# multimode: [1, 2]

2 Measures of Spread: variance & standard deviation

Center tells you where the data sits; spread tells you how scattered it is. Variance is the average squared distance from the mean, and standard deviation is its square root (back in the original units). Python gives you both a sample and a population version:

import statistics as st

data = [12, 15, 15, 18, 22, 30]

# Sample (divides by n-1) — use for a sample of a bigger group
print("variance:", round(st.variance(data), 4))   # variance: 42.2667
print("stdev:", round(st.stdev(data), 4))         # stdev: 6.5013

# Population (divides by n) — use when data IS everything
print("pvariance:", round(st.pvariance(data), 4)) # pvariance: 35.2222
print("pstdev:", round(st.pstdev(data), 4))       # pstdev: 5.9348

import statistics as st

# Two classes with the same mean but different consistency
steady = [80, 81, 79, 80, 80]
swingy = [60, 100, 70, 90, 80]

print("steady mean:", st.mean(steady))
print("swingy mean:", st.mean(swingy))
print("steady stdev:", round(st.stdev(steady), 2))
print("swingy stdev:", round(st.stdev(swingy), 2))

# ✅ Expected output:
# steady mean: 80
# swingy mean: 80
# steady stdev: 0.71
# swingy stdev: 15.81

3 Quantiles & Specialized Means

Quantiles cut sorted data into equal-sized buckets. Pass n=4 to get the three quartile cut-points (25%, 50%, 75%), or n=100 for percentiles. Python also offers faster and specialized averages:

import statistics as st

data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

# Quartile cut-points (the values at 25%, 50%, 75%)
print("quartiles:", st.quantiles(data, n=4))
# quartiles: [2.75, 5.5, 8.25]

# fmean: a faster, always-float arithmetic mean (Python 3.8+)
print("fmean:", st.fmean([2, 4, 6, 8]))     # fmean: 5.0

# geometric_mean: for growth rates / ratios
print("geometric:", st.geometric_mean([2, 4, 8]))  # geometric: 4.0

# harmonic_mean: for rates / speeds
print("harmonic:", st.harmonic_mean([40, 60]))     # harmonic: 48.0

Use fmean when you just want a fast average of floats, geometric_mean for things that multiply (like yearly growth), and harmonic_mean when averaging rates (like average speed over equal distances).

import statistics as st

# Average speed for two equal-distance legs of a trip
# (60 km/h out, 40 km/h back) — harmonic mean is correct here
print("avg speed:", st.harmonic_mean([60, 40]))

# Compound growth: 2x then 8x averages to 4x per step
print("growth:", st.geometric_mean([2, 8]))

# Percentile cut-points
data = list(range(1, 21))
print("deciles:", st.quantiles(data, n=10)[:3])

# ✅ Expected output:
# avg speed: 48.0
# growth: 4.0
# deciles: [2.1, 4.2, 6.3]

🎯 YOUR TURN: Fill in the Blanks

Replace each ___ with the correct statistics function so the output matches. Think about which "average" each comment describes.

import statistics as st

prices = [9.99, 14.99, 14.99, 19.99, 49.99]

# 1. The arithmetic average -> use ___
avg = st.___(prices)
print("avg:", round(avg, 2))

# 2. The middle value -> use ___
mid = st.___(prices)
print("middle:", mid)

# 3. The most common value -> use ___
common = st.___(prices)
print("common:", common)

# Expected output:
# avg: 21.99
# middle: 14.99
# common: 14.99

Common Errors

❌ Calling a statistic on an empty list

st.mean([])   # StatisticsError: mean requires at least one data point

✅ Guard for emptiness first

data = []
avg = st.mean(data) if data else 0
print(avg)    # 0

❌ Expecting mode to handle ties

st.mode([1, 1, 2, 2])   # returns just 1, silently ignoring the tie

✅ Use multimode when ties are possible

print(st.multimode([1, 1, 2, 2]))   # [1, 2]

❌ Mixing up sample and population spread

# Using pstdev on a SAMPLE under-reports the real spread

✅ Use stdev for samples, pstdev only for full populations

sample = [2, 4, 4, 4, 5, 5, 7, 9]
print(round(st.stdev(sample), 4))    # 2.1381  (sample)
print(round(st.pstdev(sample), 4))   # 2.0     (population)

🎯 Mini Challenge: Grade Report

Build a small grade summary that reports the class average, the median, how spread out the scores are, and the top-quartile cutoff.

import statistics as st

grades = [55, 62, 70, 71, 78, 85, 88, 90, 94, 100]

print("Average:", round(st.mean(grades), 1))
print("Median :", st.median(grades))
print("Spread :", round(st.stdev(grades), 1))

# The 75% cut-point is the 3rd of 4 quantiles
top_quartile = st.quantiles(grades, n=4)[2]
print("Top 25% starts at:", top_quartile)

# ✅ Expected output:
# Average: 79.3
# Median : 81.5
# Spread : 14.6
# Top 25% starts at: 91.0

📚 Keep Learning

• statistics — Mathematical statistics functions (official docs)
• statistics.quantiles — splitting data into intervals
• math — the lower-level math functions statistics builds on

Frequently Asked Questions

Lesson complete — you can summarize data with pure Python!

You can now find the mean, median, and mode, measure spread with sample (stdev) and population (pstdev) standard deviation, split data with quantiles, and choose specialized means like fmean and geometric_mean — all without any external libraries.

Practice quiz

Continue this course

• Previous: Checkpoint: Concurrency & I/O
• Next: The operator Module — Use itemgetter, attrgetter and operator functions for fast, clean code
• Quick reference: Python cheat sheet

Frequently asked questions

What is the statistics module in Python?

It's a built-in standard-library module that gives you common statistical calculations — mean, median, mode, standard deviation, variance, quantiles and more — without installing anything. It works on plain Python lists of numbers and is perfect for small to medium datasets where pulling in numpy or pandas would be overkill.

What's the difference between stdev and pstdev?

stdev (and variance) compute the SAMPLE standard deviation, which divides by n-1 and is what you want when your data is a sample drawn from a larger population. pstdev (and pvariance) compute the POPULATION value, dividing by n, and are correct when your data IS the entire population. The sample versions give a slightly larger number to correct for the bias of estimating from a sample.

When should I use statistics instead of numpy or pandas?

Reach for statistics when you have a small dataset, want zero dependencies, or are writing a script that should run anywhere with just Python installed. Switch to numpy or pandas when you have large arrays (thousands+ of values), need vectorized speed, or already work with DataFrames — those libraries are dramatically faster on big data but add install weight.

What does mode do when there are several most-common values?

statistics.mode returns the single first most-common value it encounters. If you expect ties — several values sharing the top frequency — use statistics.multimode instead, which returns a list of all the most-common values. This avoids surprises when your data genuinely has more than one peak.