Python statistics Module

from statistics import mean
 
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
print(mean(data))  # 5.5

from statistics import median, median_low, median_high
 
odd = [1, 3, 5, 7, 9]
even = [1, 2, 3, 4, 5, 6]
 
print(median(odd))       # 5
print(median(even))      # 3.5 (average of middle two)
print(median_low(even))  # 3 (lower of middle two)
print(median_high(even)) # 4 (higher of middle two)

from statistics import mode, multimode
 
data = [1, 2, 2, 3, 3, 3, 4]
print(mode(data))  # 3
 
# Multiple modes
bimodal = [1, 1, 2, 2, 3]
print(multimode(bimodal))  # [1, 2]

from statistics import geometric_mean
 
returns = [1.1, 1.2, 0.9, 1.15]  # 10%, 20%, -10%, 15%
avg_return = geometric_mean(returns)
print(f"Average return factor: {avg_return:.4f}")

from statistics import harmonic_mean
 
speeds = [60, 40]  # mph for equal distances
avg_speed = harmonic_mean(speeds)
print(f"Average speed: {avg_speed:.1f} mph")  # 48.0

from statistics import variance, pvariance
 
data = [2, 4, 4, 4, 5, 5, 7, 9]
 
# Sample variance (n-1)
print(variance(data))   # 4.571...
 
# Population variance (n)
print(pvariance(data))  # 4.0

from statistics import stdev, pstdev
 
data = [2, 4, 4, 4, 5, 5, 7, 9]
 
# Sample standard deviation
print(stdev(data))   # 2.138...
 
# Population standard deviation
print(pstdev(data))  # 2.0

from statistics import quantiles
 
data = list(range(1, 101))  # 1 to 100
 
# Quartiles (default n=4)
q = quantiles(data)
print(q)  # [25.5, 50.5, 75.5]
 
# Deciles
d = quantiles(data, n=10)
print(d)  # 9 cut points
 
# Percentiles
p = quantiles(data, n=100)
print(p[49])  # 50th percentile

from statistics import covariance, correlation
 
x = [1, 2, 3, 4, 5]
y = [2, 4, 5, 4, 5]
 
# How variables move together
cov = covariance(x, y)
print(f"Covariance: {cov}")
 
# Correlation (-1 to 1)
corr = correlation(x, y)
print(f"Correlation: {corr:.3f}")

from statistics import linear_regression
 
x = [1, 2, 3, 4, 5]
y = [2, 4, 5, 4, 5]
 
slope, intercept = linear_regression(x, y)
print(f"y = {slope:.2f}x + {intercept:.2f}")
 
# Predict
predict_x = 6
predict_y = slope * predict_x + intercept
print(f"At x=6, y={predict_y:.2f}")

from statistics import NormalDist
 
# Create from parameters
dist = NormalDist(mu=100, sigma=15)  # IQ distribution
 
# From data
data = [98, 102, 101, 99, 100, 103, 97]
dist = NormalDist.from_samples(data)
 
# Properties
print(f"Mean: {dist.mean}")
print(f"Stdev: {dist.stdev}")
print(f"Variance: {dist.variance}")
 
# Probability density at a point
print(f"PDF at 100: {dist.pdf(100):.4f}")
 
# Cumulative distribution
print(f"CDF at 100: {dist.cdf(100):.4f}")  # Prob of being <= 100
 
# Inverse CDF (quantile)
print(f"85th percentile: {dist.inv_cdf(0.85):.2f}")

from statistics import NormalDist
 
iq = NormalDist(100, 15)
 
# What percentage scores above 130?
above_130 = 1 - iq.cdf(130)
print(f"Above 130: {above_130:.2%}")
 
# What score is the top 1%?
top_1_percent = iq.inv_cdf(0.99)
print(f"Top 1%: {top_1_percent:.1f}")
 
# Overlap between two distributions
test_a = NormalDist(100, 15)
test_b = NormalDist(105, 12)
overlap = test_a.overlap(test_b)
print(f"Distribution overlap: {overlap:.2%}")

from statistics import (
    mean, median, stdev, quantiles, NormalDist
)
 
scores = [72, 85, 90, 78, 92, 88, 76, 95, 82, 89,
          91, 73, 87, 84, 79, 93, 81, 86, 77, 94]
 
print(f"Mean: {mean(scores):.1f}")
print(f"Median: {median(scores)}")
print(f"Std Dev: {stdev(scores):.2f}")
 
q = quantiles(scores)
print(f"Q1: {q[0]:.1f}, Q2: {q[1]:.1f}, Q3: {q[2]:.1f}")
 
# Fit normal distribution
dist = NormalDist.from_samples(scores)
 
# What's the probability of scoring above 90?
prob_above_90 = 1 - dist.cdf(90)
print(f"Probability above 90: {prob_above_90:.2%}")