Calculating arithmetic mean one type of average in Python

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Arithmetic Mean

Average Calculation

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Calculating arithmetic mean one type of average in Python

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Introduction

The arithmetic mean (average) of a collection of numbers is the sum divided by the count. In Python, the most straightforward way is sum(data) / len(data), but the standard library provides statistics.mean() for correctness with edge cases, and NumPy provides numpy.mean() for high-performance computation on large arrays. Each approach has different tradeoffs in precision, performance, and handling of empty inputs. This article covers all common methods with their appropriate use cases.

Using sum() and len()

python

1numbers = [10, 20, 30, 40, 50]
2
3mean = sum(numbers) / len(numbers)
4print(mean)  # 30.0
5
6# Works with floats
7prices = [9.99, 14.50, 3.75, 22.00]
8avg_price = sum(prices) / len(prices)
9print(avg_price)  # 12.56
10
11# Works with negative numbers
12temps = [-5, 3, 7, -2, 15, 8]
13avg_temp = sum(temps) / len(temps)
14print(f"{avg_temp:.1f}")  # 4.3

This approach raises ZeroDivisionError on empty lists:

python

1empty = []
2# mean = sum(empty) / len(empty)  # ZeroDivisionError
3
4# Safe version
5mean = sum(empty) / len(empty) if empty else 0

Using statistics.mean()

The statistics module (Python 3.4+) handles Fraction and Decimal types correctly:

python

1from statistics import mean
2
3numbers = [10, 20, 30, 40, 50]
4print(mean(numbers))  # 30
5
6# Works with any iterable of numbers
7print(mean((1, 2, 3)))              # 2
8print(mean(range(1, 11)))           # 5.5
9
10# Handles Fraction and Decimal precisely
11from fractions import Fraction
12fracs = [Fraction(1, 3), Fraction(2, 3), Fraction(1, 6)]
13print(mean(fracs))  # 7/18 (exact, no floating-point error)
14
15from decimal import Decimal
16prices = [Decimal("9.99"), Decimal("14.50"), Decimal("3.75")]
17print(mean(prices))  # 9.413333333333333333333333333 (Decimal precision)

statistics.mean() raises StatisticsError on empty input:

python

1from statistics import mean, StatisticsError
2
3try:
4    mean([])
5except StatisticsError as e:
6    print(e)  # mean requires at least one data point

Using numpy.mean()

NumPy is the best choice for large datasets and multi-dimensional arrays:

python

1import numpy as np
2
3# Basic usage
4data = [10, 20, 30, 40, 50]
5print(np.mean(data))  # 30.0
6
7# NumPy arrays
8arr = np.array([1.5, 2.5, 3.5, 4.5])
9print(arr.mean())  # 3.0
10
11# Large dataset (much faster than pure Python)
12big_data = np.random.randn(1_000_000)
13print(np.mean(big_data))  # ~0.0 (standard normal)
14
15# Multi-dimensional arrays
16matrix = np.array([[1, 2, 3],
17                   [4, 5, 6],
18                   [7, 8, 9]])
19
20print(np.mean(matrix))          # 5.0 (all elements)
21print(np.mean(matrix, axis=0))  # [4. 5. 6.] (column means)
22print(np.mean(matrix, axis=1))  # [2. 5. 8.] (row means)

Weighted Mean

python

1import numpy as np
2
3scores = [85, 90, 78, 92]
4weights = [0.2, 0.3, 0.2, 0.3]
5
6weighted_avg = np.average(scores, weights=weights)
7print(weighted_avg)  # 87.1
8
9# Manual calculation for verification
10manual = sum(s * w for s, w in zip(scores, weights)) / sum(weights)
11print(manual)  # 87.1

Using functools.reduce()

A functional programming approach:

python

1from functools import reduce
2
3numbers = [10, 20, 30, 40, 50]
4
5total = reduce(lambda acc, x: acc + x, numbers)
6mean = total / len(numbers)
7print(mean)  # 30.0
8
9# Or in a single expression
10mean = reduce(lambda acc, x: acc + x, numbers) / len(numbers)

This is less readable than sum() / len() and generally not preferred for this task.

Running (Cumulative) Mean

python

1# Running mean — average up to each index
2numbers = [10, 20, 30, 40, 50]
3
4running_means = []
5for i in range(len(numbers)):
6    running_means.append(sum(numbers[:i+1]) / (i + 1))
7
8print(running_means)  # [10.0, 15.0, 20.0, 25.0, 30.0]
9
10# NumPy approach
11import numpy as np
12arr = np.array(numbers)
13running = np.cumsum(arr) / np.arange(1, len(arr) + 1)
14print(running)  # [10. 15. 20. 25. 30.]

Other Types of Averages

python

1from statistics import mean, median, mode, harmonic_mean, geometric_mean
2
3data = [2, 4, 4, 4, 5, 5, 7, 9]
4
5print(f"Arithmetic mean: {mean(data)}")       # 5.0
6print(f"Median: {median(data)}")              # 4.5
7print(f"Mode: {mode(data)}")                  # 4
8print(f"Harmonic mean: {harmonic_mean(data):.2f}")   # 3.76
9print(f"Geometric mean: {geometric_mean(data):.2f}") # 4.30 (Python 3.8+)

Average Type	Formula	Use Case
Arithmetic mean	Sum / Count	General-purpose average
Median	Middle value	Robust to outliers
Mode	Most frequent	Categorical data
Harmonic mean	n / (sum of 1/x)	Rates, speeds, ratios
Geometric mean	nth root of product	Growth rates, percentages

Performance Comparison

python

1import timeit
2import numpy as np
3from statistics import mean as stats_mean
4
5data_list = list(range(100_000))
6data_array = np.array(data_list)
7
8# Pure Python: sum/len
9t1 = timeit.timeit(lambda: sum(data_list) / len(data_list), number=100)
10
11# statistics.mean
12t2 = timeit.timeit(lambda: stats_mean(data_list), number=100)
13
14# numpy.mean on list (includes conversion)
15t3 = timeit.timeit(lambda: np.mean(data_list), number=100)
16
17# numpy.mean on array (fastest)
18t4 = timeit.timeit(lambda: np.mean(data_array), number=100)
19
20# Typical results:
21# sum/len:         ~0.05s
22# statistics.mean: ~0.50s (slower due to type handling)
23# np.mean(list):   ~0.15s (list-to-array conversion overhead)
24# np.mean(array):  ~0.001s (fastest)

Common Pitfalls

Using sum()/len() on empty lists: This raises ZeroDivisionError. Always check if data: first, or use statistics.mean() which raises a descriptive StatisticsError instead.
Integer division in Python 2: In Python 2, sum([1,2,3]) / len([1,2,3]) returns 2 (integer division). Use from __future__ import division or cast to float. Python 3 always returns a float for /.
Floating-point precision with sum()/len(): Summing many floats accumulates rounding errors. statistics.mean() uses a more accurate algorithm internally. For financial calculations, use Decimal types with statistics.mean().
Calling np.mean() on a Python list repeatedly: Each call converts the list to a NumPy array first, adding overhead. Convert to a NumPy array once and reuse it if you need multiple operations.
Confusing np.mean() with np.average(): np.mean() computes an unweighted average. np.average() supports an optional weights parameter for weighted means. They return different results when weights are provided.

Summary

Use sum(data) / len(data) for simple, quick calculations on lists
Use statistics.mean() for type-safe computation with Fraction, Decimal, or when descriptive error handling is needed
Use numpy.mean() for large datasets and multi-dimensional arrays (fastest on NumPy arrays)
Use numpy.average(data, weights=w) for weighted means
Always handle empty inputs — sum()/len() raises ZeroDivisionError, statistics.mean() raises StatisticsError

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Step through 300+ coding interview problems with animated visualisers that show the data structure changing as the code runs. The Blind 75 are free.

Practice algorithms

Calculating arithmetic mean one type of average in Python

Data Structures & Algorithms practice on Codemia

Introduction

Using sum() and len()

Using statistics.mean()

Using numpy.mean()

Weighted Mean

Using functools.reduce()

Running (Cumulative) Mean

Other Types of Averages

Performance Comparison

Common Pitfalls

Summary

Related reading

Tackling System Design Interview Problems

No course covers this one yet

Data Structures & Algorithms practice on Codemia