statistics Library

The statistics library provides functions for calculating mathematical statistics of numeric data, compatible with Python’s statistics module.

Import

    
import statistics

Available Functions

Function	Description
`mean(data)`	Arithmetic mean (average)
`fmean(data)`	Float mean (same as mean, returns float)
`geometric_mean(data)`	Geometric mean
`harmonic_mean(data)`	Harmonic mean
`median(data)`	Median (middle value)
`mode(data)`	Mode (most common value)
`stdev(data)`	Sample standard deviation
`variance(data)`	Sample variance

Functions

Averages

mean(data)

Calculate the arithmetic mean (average) of data.

    
statistics.mean([1, 2, 3, 4, 5])  # Returns 3.0
statistics.mean([10.5, 20.5, 30.5])  # Returns 20.5

fmean(data)

Calculate the arithmetic mean of data (same as mean, returns float).

    
statistics.fmean([1, 2, 3, 4, 5])  # Returns 3.0

geometric_mean(data)

Calculate the geometric mean of data.

    
statistics.geometric_mean([1, 2, 4, 8])  # Returns ~2.83
statistics.geometric_mean([1, 3, 9, 27])  # Returns 5.196...

harmonic_mean(data)

Calculate the harmonic mean of data.

    
statistics.harmonic_mean([1, 2, 4])  # Returns ~1.71

Central Tendency

median(data)

Calculate the median (middle value) of data.

    
statistics.median([1, 3, 5, 7, 9])  # Returns 5.0 (odd count)
statistics.median([1, 2, 3, 4])  # Returns 2.5 (even count)

mode(data)

Calculate the mode (most common value) of data.

    
statistics.mode([1, 2, 2, 3, 3, 3])  # Returns 3
statistics.mode(["a", "b", "b"])  # Returns "b"

Measures of Spread

variance(data)

Calculate the sample variance of data.

    
data = [2, 4, 4, 4, 5, 5, 7, 9]
statistics.variance(data)  # Returns ~4.57

pvariance(data)

Calculate the population variance of data.

    
data = [2, 4, 4, 4, 5, 5, 7, 9]
statistics.pvariance(data)  # Returns 4.0

stdev(data)

Calculate the sample standard deviation.

    
data = [2, 4, 4, 4, 5, 5, 7, 9]
statistics.stdev(data)  # Returns ~2.14

pstdev(data)

Calculate the population standard deviation.

    
data = [2, 4, 4, 4, 5, 5, 7, 9]
statistics.pstdev(data)  # Returns 2.0

Examples

Basic Statistics

    
import statistics

grades = [85, 90, 78, 92, 88, 76, 95, 89]

avg = statistics.mean(grades)
med = statistics.median(grades)
std = statistics.stdev(grades)

print(f"Average: {avg}")
print(f"Median: {med}")
print(f"Std Dev: {std}")

Comparing Sample vs Population Statistics

    
import statistics

data = [2, 4, 4, 4, 5, 5, 7, 9]

# Sample statistics (use when data is a sample)
sample_var = statistics.variance(data)
sample_std = statistics.stdev(data)

# Population statistics (use when data is the entire population)
pop_var = statistics.pvariance(data)
pop_std = statistics.pstdev(data)

Finding the Mode

    
import statistics

responses = ["yes", "no", "yes", "yes", "no", "yes"]
most_common = statistics.mode(responses)  # Returns "yes"

Notes

All functions require at least one data point (except variance/stdev which require at least 2)
The mode() function returns the first mode encountered if there are multiple modes
For sample statistics, use variance() and stdev()
For population statistics, use pvariance() and pstdev()

Python Compatibility

This library implements a subset of Python’s statistics module:

Function	Supported
mean	✅
fmean	✅
geometric_mean	✅
harmonic_mean	✅
median	✅
median_low	❌
median_high	❌
median_grouped	❌
mode	✅
multimode	❌
variance	✅
pvariance	✅
stdev	✅
pstdev	✅
quantiles	❌
NormalDist	❌

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