Python ilə statistika

import numpy as np
from scipy import stats

minutes = np.array([12, 15, 11, 14, 13, 45, 13, 16, 14, 13])
print('mean  :', minutes.mean())
print('median:', np.median(minutes))
print('mode  :', stats.mode(minutes, keepdims=False).mode)
print('var   :', round(minutes.var(ddof=1), 2))
print('std   :', round(minutes.std(ddof=1), 2))
q1, q3 = np.percentile(minutes, [25, 75])
iqr = q3 - q1
print('Q1, Q3, IQR:', q1, q3, iqr)
low, high = q1 - 1.5 * iqr, q3 + 1.5 * iqr
print('outliers:', minutes[(minutes < low) | (minutes > high)])

from scipy import stats

scores = stats.norm(loc=70, scale=10)
print(round(scores.cdf(85), 4))
print(round(scores.sf(85), 4))
print(round(scores.cdf(80) - scores.cdf(60), 4))
print(round(scores.ppf(0.90), 2))
z = (85 - 70) / 10
print(z, round(stats.norm.cdf(z), 4))

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(1)
population = rng.exponential(scale=10, size=100_000)
means = rng.choice(population, size=(5000, 30)).mean(axis=1)
print(f'population: mean {population.mean():.2f}, std {population.std():.2f}')
print(f'sample means: mean {means.mean():.2f}, std {means.std():.2f}')
print(f'sigma / sqrt(n) = {population.std() / np.sqrt(30):.2f}')

fig, (a, b) = plt.subplots(1, 2, figsize=(8, 3), layout='constrained')
a.hist(population, bins=50)
a.set_title('Population (skewed)')
b.hist(means, bins=40)
b.set_title('Means of samples, n = 30')
plt.show()

import numpy as np
from scipy import stats

packs = np.array([99.2, 100.4, 98.7, 100.9, 99.5, 100.1, 99.8, 98.9, 100.6, 99.4])
n = packs.size
mean = packs.mean()
s = packs.std(ddof=1)
se = s / np.sqrt(n)
t_crit = stats.t.ppf(0.975, df=n - 1)
print(f'mean = {mean:.2f} g, s = {s:.3f} g, SE = {se:.3f} g')
print(f't* = {t_crit:.3f}')
print(f'95% CI: [{mean - t_crit * se:.2f}; {mean + t_crit * se:.2f}] g')
low, high = stats.t.interval(0.95, df=n - 1, loc=mean, scale=se)
print(round(low, 2), round(high, 2))

import numpy as np
from scipy import stats

packs = np.array([99.2, 100.4, 98.7, 100.9, 99.5, 100.1, 99.8, 98.9, 100.6, 99.4])
res1 = stats.ttest_1samp(packs, popmean=100)
print(f'one-sample: t = {res1.statistic:.3f}, p = {res1.pvalue:.3f}')

group_a = np.array([72, 85, 78, 90, 66, 81, 77, 88, 74, 83])
group_b = np.array([80, 91, 86, 94, 79, 88, 85, 97, 82, 90])
print(group_a.mean(), group_b.mean())
res2 = stats.ttest_ind(group_b, group_a, equal_var=False)
print(f'Welch: t = {res2.statistic:.3f}, p = {res2.pvalue:.4f}')

import numpy as np
from scipy import stats

hours = np.array([1, 2, 2, 3, 4, 5, 5, 6, 7, 8])
score = np.array([52, 55, 61, 60, 68, 70, 75, 74, 82, 88])
r, p = stats.pearsonr(hours, score)
rho, _ = stats.spearmanr(hours, score)
print(f'Pearson r = {r:.3f}, p = {p:.1e}')
print(f'Spearman rho = {rho:.3f}')
print(f'r squared = {r ** 2:.3f}')
print(np.corrcoef(hours, score).round(3))

import numpy as np

data = np.array([48, 52, 50, 47, 53, 51, 49, 95, 50, 52])
# line 1: mean (1 decimal), median, sample std (2 decimals)
# line 2: outliers as a list

import numpy as np
from scipy import stats

sample = np.array([23.1, 24.5, 22.8, 25.0, 23.9, 24.2, 23.5, 24.8])
# mean, then the 95% confidence interval