3.3. Math Statistics¶
statisticsmodule
3.3.1. Mean¶
Function |
Description |
|---|---|
|
Arithmetic mean ('average') of data |
|
faster, floating point variant of |
|
Harmonic mean of data |
|
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
3.3.2. Median¶
Function |
Description |
|---|---|
|
Median (middle value) of data |
|
Low median of data |
|
High median of data |
|
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
3.3.3. Mode¶
Function |
Description |
|---|---|
|
Mode (most common value) of discrete data |
|
returns a list of the most common values, since Python 3.8 |
|
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'
3.3.4. Distribution¶
Function |
Description |
|---|---|
|
tool for creating and manipulating normal distributions of a random variable |
3.3.5. Standard Deviation¶
Function |
Description |
|---|---|
|
Population standard deviation of data |
|
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
3.3.6. Variance¶
Function |
Description |
|---|---|
|
Population variance of data |
|
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
3.3.7. 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]
3.3.8. Assignments¶
"""
* Assignment: Math Statistics Stats
* Complexity: easy
* Lines of code: 11 lines
* Time: 13 min
English:
1. For columns:
a. sepal_length,
b. sepal_width,
c. petal_length,
d. petal_width.
2. Print calculated values:
a. mean,
b. median,
c. standard deviation,
d. variance.
3. Use `statistics` module from Python standard library
4. Run doctests - all must succeed
Polish:
1. Dla kolumn:
a. sepal_length,
b. sepal_width,
c. petal_length,
d. petal_width.
2. Wypisz wyliczone wartości:
a. średnią,
b. medianę,
c. odchylenie standardowe,
d. wariancję.
3. Użyj modułu `statistics` z biblioteki standardowej Python
4. Uruchom doctesty - wszystkie muszą się powieść
Hint:
* Note, that in petal_length stdev is:
a. Python 3.10: 1.8602739173624534
b. Python 3.11: 1.8602739173624532
Tests:
>>> import sys; sys.tracebacklimit = 0
>>> 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}
"""
from statistics import mean, stdev, variance, median
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'),
]
"""
* Assignment: Math Statistics Iris
* Complexity: easy
* Lines of code: 30 lines
* Time: 21 min
English:
1. Create dict `result: dict[str, dict]`
2. For each species calculate for numerical values:
a. mean,
b. median,
c. standard deviation,
d. variance.
3. Save data to `result` dict
4. Non-functional requirements:
a. 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:
a. średnią,
b. medianę,
c. odchylenie standardowe,
d. wariancję.
3. Dane zapisz w słowniku `result`
4. Wymagania niefunkcjonalne:
a. Użyj modułu `statistics` z biblioteki standardowej Python
5. Uruchom doctesty - wszystkie muszą się powieść
Tests:
>>> import sys; sys.tracebacklimit = 0
>>> 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}}}
"""
from statistics import mean, stdev, median, variance
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 = {}