12.2. Math Statistics

  • statistics module

12.2.1. Mean

Table 36. 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

Listing 422. 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 423. Harmonic mean of data
from statistics import harmonic_mean


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

12.2.2. Median

Table 37. 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 424. 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 425. 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 426. 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 427. 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 38. 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

Listing 428. 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 39. Distribution

Function

Description

statistics.NormalDist

tool for creating and manipulating normal distributions of a random variable

12.2.5. Standard Deviation

Table 40. Standard Deviation

Function

Description

statistics.pstdev()

Population standard deviation of data

statistics.stdev()

Sample standard deviation of data

Listing 429. 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 430. 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 41. Variance

Function

Description

statistics.pvariance()

Population variance of data

statistics.variance()

Sample variance of data

Listing 431. 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 432. 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. Example

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

English
  1. Use INPUT: List[tuple] from listing (see below)

  2. For columns:

    • Sepal length,

    • Sepal width,

    • Petal length,

    • Petal width.

  3. Print calculated values:

    • mean,

    • median,

    • standard deviation,

    • variance.

Polish
  1. Użyj INPUT: List[tuple] z listingu (patrz sekcja input)

  2. Dla kolumn:

    • Sepal length,

    • Sepal width,

    • Petal length,

    • Petal width.

  3. Wypisz wyliczone wartości:

    • średnią,

    • medianę,

    • odchylenie standardowe,

    • wariancję.

Non-functional requirements
  1. Use statistics

Input
INPUT = [
    ('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

English
  1. Create dict OUTPUT: Dict[str, dict]

  2. For each species calculate for numerical values:

    • mean,

    • median,

    • standard deviation,

    • variance.

  3. Save data to OUTPUT dict

Polish
  1. Stwórz słownik OUTPUT: Dict[str, dict]

  2. Dla każdego gatunku wylicz dla wartości numerycznych:

    • średnią,

    • medianę,

    • odchylenie standardowe,

    • wariancję.

  3. Dane zapisz w słowniku OUTPUT

Non-functional requirements
  1. Use statistics

Input
INPUT = [
    ('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
OUTPUT: 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': {...},
}