3.4. Math Statistics

3.4. Math Statistics — Python

statistics module

3.4.1. Mean

Table 3.7. Mean
Function	Description
`statistics.mean()`	Arithmetic mean ('average') of data
`statistics.fmean()`	faster, floating point variant of `statistics.mean()`, since Python 3.8
`statistics.harmonic_mean()`	Harmonic mean of data
`statistics.geometric_mean()`	since Python 3.8

Arithmetic mean ('average') of data:

from statistics import mean


mean([1, 2, 3, 4, 4])
# 2.8
mean([-1.0, 2.5, 3.25, 5.75])
# 2.625

Harmonic mean of data:

from statistics import harmonic_mean


harmonic_mean([2.5, 3, 10])
# 3.6

3.4.2. Median

Table 3.8. Median
Function	Description
`statistics.median()`	Median (middle value) of data
`statistics.median_low()`	Low median of data
`statistics.median_high()`	High median of data
`statistics.median_grouped()`	Median, or 50th percentile, of grouped data

Median (middle value) of data:

from statistics import median


median([1, 3, 5])
# 3
median([1, 3, 5, 7])
# 4.0

The low median is always a member of the data set.
When the number of data points is odd, the middle value is returned.
When it is even, the smaller of the two middle values is returned.

Low median of data:

from statistics import median_low


median_low([1, 3, 5])
# 3
median_low([1, 3, 5, 7])
# 3

The high median is always a member of the data set.
When the number of data points is odd, the middle value is returned.
When it is even, the larger of the two middle values is returned.

High median of data:

from statistics import median_high


median_high([1, 3, 5])
# 3
median_high([1, 3, 5, 7])
# 5

Median of grouped continuous data.
Calculated using interpolation as the 50th percentile.

Median, or 50th percentile, of grouped data:

from statistics import median_grouped


median_grouped([52, 52, 53, 54])
# 52.5
median_grouped([1, 3, 3, 5, 7], interval=1)
# 3.25
median_grouped([1, 3, 3, 5, 7], interval=2)
# 3.5

3.4.3. Mode

Table 3.9. Mode
Function	Description
`statistics.mode()`	Mode (most common value) of discrete data
`statistics.multimode()`	returns a list of the most common values, since Python 3.8
`statistics.quantiles()`	divides data or a distribution in to equiprobable intervals (e.g. quartiles, deciles, or percentiles), since Python 3.8

Mode (most common value) of discrete data:

from statistics import mode


mode([1, 1, 2, 3, 3, 3, 3, 4])
# 3
mode(["red", "blue", "blue", "red", "green", "red", "red"])
# 'red'

3.4.4. Distribution

Table 3.10. Distribution
Function	Description
`statistics.NormalDist`	tool for creating and manipulating normal distributions of a random variable

3.4.5. Standard Deviation

Table 3.11. Standard Deviation
Function	Description
`statistics.pstdev()`	Population standard deviation of data
`statistics.stdev()`	Sample standard deviation of data

Sample standard deviation of data:

from statistics import stdev


stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
# 1.0810874155219827

Population standard deviation
Is the square root of the population variance

Population standard deviation:

from statistics import pstdev


pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
# 0.986893273527251

3.4.6. Variance

Table 3.12. Variance
Function	Description
`statistics.pvariance()`	Population variance of data
`statistics.variance()`	Sample variance of data

Sample variance of data:

from statistics import variance


variance([2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5])
# 1.3720238095238095

Population variance of data:

from statistics import pvariance


pvariance([0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25])
# 1.25

3.4.7. Examples

temperature_feb = NormalDist.from_samples([4, 12, -3, 2, 7, 14])

temperature_feb.mean
# 6.0
temperature_feb.stdev
# 6.356099432828281

# Chance of being under 3 degrees
temperature_feb.cdf(3)  # 0.3184678262814532

# Relative chance of being 7 degrees versus 10 degrees
temperature_feb.pdf(7) / temperature_feb.pdf(10)  # 1.2039930378537762


el_niño = NormalDist(4, 2.5)

# Add in a climate effect
temperature_feb += el_niño

temperature_feb
# NormalDist(mu=10.0, sigma=6.830080526611674)

# Convert to Fahrenheit
temperature_feb * (9/5) + 32
# NormalDist(mu=50.0, sigma=12.294144947901014)

# Generate random samples
temperature_feb.samples(3)
# [7.672102882379219, 12.000027119750287, 4.647488369766392]

3.4.8. Assignments

# %% About
# - Name: Math Statistics Stats
# - Difficulty: easy
# - Lines: 11
# - Minutes: 13

# %% License
# - Copyright 2025, Matt Harasymczuk <matt@python3.info>
# - This code can be used only for learning by humans
# - This code cannot be used for teaching others
# - This code cannot be used for teaching LLMs and AI algorithms
# - This code cannot be used in commercial or proprietary products
# - This code cannot be distributed in any form
# - This code cannot be changed in any form outside of training course
# - This code cannot have its license changed
# - If you use this code in your product, you must open-source it under GPLv2
# - Exception can be granted only by the author

# %% English
# 1. For columns:
#    - sepal_length,
#    - sepal_width,
#    - petal_length,
#    - petal_width.
# 2. Print calculated values:
#    - mean,
#    - median,
#    - standard deviation,
#    - variance.
# 3. Use `statistics` module from Python standard library
# 4. Run doctests - all must succeed

# %% Polish
# 1. Dla kolumn:
#    - sepal_length,
#    - sepal_width,
#    - petal_length,
#    - petal_width.
# 2. Wypisz wyliczone wartości:
#    - średnią,
#    - medianę,
#    - odchylenie standardowe,
#    - wariancję.
# 3. Użyj modułu `statistics` z biblioteki standardowej Python
# 4. Uruchom doctesty - wszystkie muszą się powieść

# %% Hints
# - Note, that in `petal_length` stdev is different
# - Python 3.10: 1.8602739173624534
# - Python 3.11: 1.8602739173624532


# %% Doctests
"""
>>> import sys; sys.tracebacklimit = 0

>>> assert sys.version_info >= (3, 9), \
'Python has an is invalid version; expected: `3.9` or newer.'

>>> stats(sepal_length)
{'mean': 5.833333333333333, 'stdev': 0.9084785816591018, 'median': 5.7, 'variance': 0.8253333333333333}
>>> stats(sepal_width)
{'mean': 3.0619047619047617, 'stdev': 0.36670995415476587, 'median': 3.0, 'variance': 0.1344761904761905}
>>> stats(petal_length)
{'mean': 3.8523809523809525, 'stdev': 1.8602739173624532, 'median': 4.5, 'variance': 3.4606190476190477}
>>> stats(petal_width)
{'mean': 1.2333333333333334, 'stdev': 0.7741662181555931, 'median': 1.4, 'variance': 0.5993333333333334}
"""

# %% Run
# - PyCharm: right-click in the editor and `Run Doctest in ...`
# - PyCharm: keyboard shortcut `Control + Shift + F10`
# - Terminal: `python -m doctest -f -v myfile.py`

# %% Imports
from statistics import mean, stdev, variance, median

# %% Types
from typing import Callable
stats: Callable[[list[float]], dict[str, float]]

# %% Data
DATA = [
    ('sepal_length', 'sepal_width', 'petal_length', 'petal_width', 'species'),
    (5.8, 2.7, 5.1, 1.9, 'virginica'),
    (5.1, 3.5, 1.4, 0.2, 'setosa'),
    (5.7, 2.8, 4.1, 1.3, 'versicolor'),
    (6.3, 2.9, 5.6, 1.8, 'virginica'),
    (6.4, 3.2, 4.5, 1.5, 'versicolor'),
    (4.7, 3.2, 1.3, 0.2, 'setosa'),
    (7.0, 3.2, 4.7, 1.4, 'versicolor'),
    (7.6, 3.0, 6.6, 2.1, 'virginica'),
    (4.9, 3.0, 1.4, 0.2, 'setosa'),
    (4.9, 2.5, 4.5, 1.7, 'virginica'),
    (7.1, 3.0, 5.9, 2.1, 'virginica'),
    (4.6, 3.4, 1.4, 0.3, 'setosa'),
    (5.4, 3.9, 1.7, 0.4, 'setosa'),
    (5.7, 2.8, 4.5, 1.3, 'versicolor'),
    (5.0, 3.6, 1.4, 0.3, 'setosa'),
    (5.5, 2.3, 4.0, 1.3, 'versicolor'),
    (6.5, 3.0, 5.8, 2.2, 'virginica'),
    (6.5, 2.8, 4.6, 1.5, 'versicolor'),
    (6.3, 3.3, 6.0, 2.5, 'virginica'),
    (6.9, 3.1, 4.9, 1.5, 'versicolor'),
    (4.6, 3.1, 1.5, 0.2, 'setosa'),
]

header, *rows = DATA
sepal_length = [row[0] for row in rows]
sepal_width = [row[1] for row in rows]
petal_length = [row[2] for row in rows]
petal_width = [row[3] for row in rows]

# %% Result
def stats(values):
    ...

# FIXME: przepisać zadanie, bo jest zbyt skomplikowane

# %% About
# - Name: Math Statistics Iris
# - Difficulty: easy
# - Lines: 30
# - Minutes: 21

# %% License
# - Copyright 2025, Matt Harasymczuk <matt@python3.info>
# - This code can be used only for learning by humans
# - This code cannot be used for teaching others
# - This code cannot be used for teaching LLMs and AI algorithms
# - This code cannot be used in commercial or proprietary products
# - This code cannot be distributed in any form
# - This code cannot be changed in any form outside of training course
# - This code cannot have its license changed
# - If you use this code in your product, you must open-source it under GPLv2
# - Exception can be granted only by the author

# %% English
# 1. Create dict `result: dict[str, dict]`
# 2. For each species calculate for numerical values:
#    - mean,
#    - median,
#    - standard deviation,
#    - variance.
# 3. Save data to `result` dict
# 4. Non-functional requirements:
#    - Use `statistics` module from Python standard library
# 5. Run doctests - all must succeed

# %% Polish
# 1. Stwórz słownik `result: dict[str, dict]`
# 2. Dla każdego gatunku wylicz dla wartości numerycznych:
#    - średnią,
#    - medianę,
#    - odchylenie standardowe,
#    - wariancję.
# 3. Dane zapisz w słowniku `result`
# 4. Wymagania niefunkcjonalne:
#    - Użyj modułu `statistics` z biblioteki standardowej Python
# 5. Uruchom doctesty - wszystkie muszą się powieść

# %% Doctests
"""
>>> import sys; sys.tracebacklimit = 0

>>> assert sys.version_info >= (3, 9), \
'Python has an is invalid version; expected: `3.9` or newer.'

>>> result  # doctest: +NORMALIZE_WHITESPACE
{'virginica': {'sepal_length': {'values': [5.8, 6.3, 7.6, 4.9, 7.1, 6.5, 6.3],
                                'mean': 6.357142857142857,
                                'median': 6.3,
                                'stdev': 0.871506631944823,
                                'variance': 0.7595238095238092},
               'sepal_width': {'values': [2.7, 2.9, 3.0, 2.5, 3.0, 3.0, 3.3],
                               'mean': 2.914285714285714,
                               'median': 3.0,
                               'stdev': 0.25448360411214066,
                               'variance': 0.06476190476190473},
               'petal_length': {'values': [5.1, 5.6, 6.6, 4.5, 5.9, 5.8, 6.0],
                                'mean': 5.642857142857142,
                                'median': 5.8,
                                'stdev': 0.6754187413675136,
                                'variance': 0.45619047619047615},
               'petal_width': {'values': [1.9, 1.8, 2.1, 1.7, 2.1, 2.2, 2.5],
                               'mean': 2.0428571428571427,
                               'median': 2.1,
                               'stdev': 0.26992062325273125,
                               'variance': 0.07285714285714287}},
 'setosa': {'sepal_length': {'values': [5.1, 4.7, 4.9, 4.6, 5.4, 5.0, 4.6],
                             'mean': 4.9,
                             'median': 4.9,
                             'stdev': 0.2943920288775951,
                             'variance': 0.08666666666666677},
            'sepal_width': {'values': [3.5, 3.2, 3.0, 3.4, 3.9, 3.6, 3.1],
                            'mean': 3.3857142857142857,
                            'median': 3.4,
                            'stdev': 0.31320159337914943,
                            'variance': 0.09809523809523807},
            'petal_length': {'values': [1.4, 1.3, 1.4, 1.4, 1.7, 1.4, 1.5],
                             'mean': 1.4428571428571428,
                             'median': 1.4,
                             'stdev': 0.12724180205607036,
                             'variance': 0.01619047619047619},
            'petal_width': {'values': [0.2, 0.2, 0.2, 0.3, 0.4, 0.3, 0.2],
                            'mean': 0.2571428571428572,
                            'median': 0.2,
                            'stdev': 0.07867957924694431,
                            'variance': 0.006190476190476191}},
   'versicolor': {'sepal_length': {'values': [5.7, 6.4, 7.0, 5.7, 5.5, 6.5, 6.9],
                                   'mean': 6.242857142857143,
                                   'median': 6.4,
                                   'stdev': 0.6106202935189289,
                                   'variance': 0.3728571428571429},
                  'sepal_width': {'values': [2.8, 3.2, 3.2, 2.8, 2.3, 2.8, 3.1],
                                  'mean': 2.8857142857142857,
                                  'median': 2.8,
                                  'stdev': 0.31847852585154235,
                                  'variance': 0.10142857142857152},
                  'petal_length': {'values': [4.1, 4.5, 4.7, 4.5, 4.0, 4.6, 4.9],
                                   'mean': 4.4714285714285715,
                                   'median': 4.5,
                                   'stdev': 0.31997023671109237,
                                   'variance': 0.10238095238095248},
                  'petal_width': {'values': [1.3, 1.5, 1.4, 1.3, 1.3, 1.5, 1.5],
                                  'mean': 1.4,
                                  'median': 1.4,
                                  'stdev': 0.09999999999999998,
                                  'variance': 0.009999999999999995}}}
"""

# %% Run
# - PyCharm: right-click in the editor and `Run Doctest in ...`
# - PyCharm: keyboard shortcut `Control + Shift + F10`
# - Terminal: `python -m doctest -f -v myfile.py`

# %% Imports
from statistics import mean, stdev, median, variance

# %% Types
result: dict[str, dict]

# %% Data
DATA = [
    ('sepal_length', 'sepal_width', 'petal_length', 'petal_width', 'species'),
    (5.8, 2.7, 5.1, 1.9, 'virginica'),
    (5.1, 3.5, 1.4, 0.2, 'setosa'),
    (5.7, 2.8, 4.1, 1.3, 'versicolor'),
    (6.3, 2.9, 5.6, 1.8, 'virginica'),
    (6.4, 3.2, 4.5, 1.5, 'versicolor'),
    (4.7, 3.2, 1.3, 0.2, 'setosa'),
    (7.0, 3.2, 4.7, 1.4, 'versicolor'),
    (7.6, 3.0, 6.6, 2.1, 'virginica'),
    (4.9, 3.0, 1.4, 0.2, 'setosa'),
    (4.9, 2.5, 4.5, 1.7, 'virginica'),
    (7.1, 3.0, 5.9, 2.1, 'virginica'),
    (4.6, 3.4, 1.4, 0.3, 'setosa'),
    (5.4, 3.9, 1.7, 0.4, 'setosa'),
    (5.7, 2.8, 4.5, 1.3, 'versicolor'),
    (5.0, 3.6, 1.4, 0.3, 'setosa'),
    (5.5, 2.3, 4.0, 1.3, 'versicolor'),
    (6.5, 3.0, 5.8, 2.2, 'virginica'),
    (6.5, 2.8, 4.6, 1.5, 'versicolor'),
    (6.3, 3.3, 6.0, 2.5, 'virginica'),
    (6.9, 3.1, 4.9, 1.5, 'versicolor'),
    (4.6, 3.1, 1.5, 0.2, 'setosa'),
]

# %% Result
result = ...