Python
import statistics as stats

data = [2.5, 3.6, 4.1, 4.1, 5.8, 6.2, 7.0]

stats.mean(data)        # 4.757142857142857
stats.median(data)      # 4.1
stats.mode(data)        # 4.1
stats.stdev(data)       # sample standard deviation
stats.variance(data)    # sample variance

Use this module for quick, dependency-free statistical calculations on small-to-medium datasets. For heavy numerical work (large arrays, matrix ops), prefer NumPy/SciPy instead.

Progress:

• Step 1: Identify whether data is a full population or a sample
• Step 2: Choose the right averaging function (mean, median, mode, or variants)
• Step 3: Choose variance/stdev function matching population vs sample
• Step 4: Handle multiple datasets (correlation, covariance, linear regression) if needed
• Step 5: Consider NormalDist for distribution-based calculations
• Step 6: Validate results and handle edge cases (empty data, single value, non-numeric input)

Step 1: Population vs Sample

• Sample (subset of a larger population, most common case): use stdev, variance
• Population (complete dataset): use pstdev, pvariance

Step 2: Averages

Step 3: Spread

Pass a precomputed mean via xbar/mu to avoid recomputation across multiple calls.

Step 4: Relationships Between Datasets

Python
x = [1, 2, 3, 4, 5]
y = [2, 4, 5, 4, 5]

stats.covariance(x, y)              # joint variability
stats.correlation(x, y)             # Pearson correlation, -1 to 1
stats.correlation(x, y, method="ranked")  # Spearman rank correlation (3.12+)
stats.linear_regression(x, y)       # LinearRegression(slope, intercept)

Step 5: Distributions with NormalDist

Python
from statistics import NormalDist

nd = NormalDist.from_samples(data)   # fit from data
nd = NormalDist(mu=100, sigma=15)    # or specify directly

nd.pdf(110)          # probability density at x
nd.cdf(110)          # P(X <= 110)
nd.inv_cdf(0.95)     # value at 95th percentile
nd.zscore(120)       # standardized score

# Combining/comparing distributions
nd1 = NormalDist(90, 12)
nd2 = NormalDist(100, 15)
(nd1 + nd2)                      # sum of independent normals
nd1.overlap(nd2)                 # overlap coefficient (0-1)

Also available: quantiles(data, n=4) for quartiles/percentiles without fitting a full distribution.

Step 6: Edge Cases

• Empty data → raises StatisticsError
• mode/multimode work on any hashable data, not just numbers
• Functions accept Decimal and Fraction for exact arithmetic
• variance/stdev require at least 2 data points (sample stats need N-1 denominator)