12.2. Math Statistics

• statistics module

12.2.1. Mean

Table 12.1. Mean

Function	Description
statistics.mean()	Arithmetic mean ('average') of data
statistics.fmean()	faster, floating point variant of statistics.mean(), since .. versionadded:: Python 3.8
statistics.harmonic_mean()	Harmonic mean of data
statistics.geometric_mean()	New in version Python: 3.8

Listing 12.2. 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

Listing 12.3. Harmonic mean of data

from statistics import harmonic_mean


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

12.2.2. Median

Table 12.2. 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

Listing 12.4. 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.

Listing 12.5. 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.

Listing 12.6. 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.

Listing 12.7. 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

12.2.3. Mode

Table 12.3. Mode

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

Listing 12.8. 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'

12.2.4. Distribution

Table 12.4. Distribution

Function	Description
statistics.NormalDist	tool for creating and manipulating normal distributions of a random variable

12.2.5. Standard Deviation

Table 12.5. Standard Deviation

Function	Description
statistics.pstdev()	Population standard deviation of data
statistics.stdev()	Sample standard deviation of data

Listing 12.9. 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

Listing 12.10. Population standard deviation

from statistics import pstdev


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

12.2.6. Variance

Table 12.6. Variance

Function	Description
statistics.pvariance()	Population variance of data
statistics.variance()	Sample variance of data

Listing 12.11. 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

Listing 12.12. 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

12.2.7. 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]

12.2.8. Assignments

12.2.8.1. Column Stats

• Complexity level: easy

• Lines of code to write: 30 lines

• Estimated time of completion: 30 min

• Solution: solution/statistics_column_stats.py

English

1. Use data from "Input" section (see below)

2. For columns:

   • Sepal length,

   • Sepal width,

   • Petal length,

   • Petal width.

3. Print calculated values:

   • mean,

   • median,

   • standard deviation,

   • variance.

4. Non-functional requirements:

   • Use statistics module from Python standard library

Polish

1. Użyj danych z sekcji "Input" (patrz poniżej)

2. Dla kolumn:

   • Sepal length,

   • Sepal width,

   • Petal length,

   • Petal width.

3. Wypisz wyliczone wartości:

   • średnią,

   • medianę,

   • odchylenie standardowe,

   • wariancję.

4. Wymagania niefunkcjonalne:

   • Użyj modułu statistics z biblioteki standardowej Python

Input

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'),
]

12.2.8.2. Iris Stats

• Complexity level: easy

• Lines of code to write: 30 lines

• Estimated time of completion: 30 min

• Solution: solution/statistics_iris.py

English

1. Use data from "Input" section (see below)

2. Create dict result: Dict[str, dict]

3. For each species calculate for numerical values:

   • mean,

   • median,

   • standard deviation,

   • variance.

4. Save data to result dict

5. Compare result with "Output" section (see below)

6. Non-functional requirements:

   • Use statistics module from Python standard library

Polish

1. Użyj danych z sekcji "Input" (patrz poniżej)

2. Stwórz słownik result: Dict[str, dict]

3. Dla każdego gatunku wylicz dla wartości numerycznych:

   • średnią,

   • medianę,

   • odchylenie standardowe,

   • wariancję.

4. Dane zapisz w słowniku result

5. Porównaj wyniki z sekcją "Output" (patrz poniżej)

6. Wymagania niefunkcjonalne:

   • Użyj modułu statistics z biblioteki standardowej Python

Input

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'),
]

Output

result: Dict[str, dict] = {
    'setosa': {
        'Sepal length': {'mean': 4.9,
                         'median': 4.9,
                         'stdev': 0.2943920288775951,
                         'values': [5.1, 4.7, 4.9, 4.6, 5.4, 5.0, 4.6],
                         'variance': 0.08666666666666677},
        'Sepal width':  {'mean': 3.3857142857142857,
                         'median': 3.4,
                         'stdev': 0.31320159337914943,
                         'values': [3.5, 3.2, 3.0, 3.4, 3.9, 3.6, 3.1],
                         'variance': 0.09809523809523807}},
        'Petal length': {'mean': 1.4428571428571428,
                         'median': 1.4,
                         'stdev': 0.12724180205607036,
                         'values': [1.4, 1.3, 1.4, 1.4, 1.7, 1.4, 1.5],
                         'variance': 0.01619047619047619},
        'Petal width':  {'mean': 0.2571428571428572,
                         'median': 0.2,
                         'stdev': 0.07867957924694431,
                         'values': [0.2, 0.2, 0.2, 0.3, 0.4, 0.3, 0.2],
                         'variance': 0.006190476190476191},
    'virginica': {...},
    'versicolor': {...},
}