Python

These assume import statistics as st, import numpy as np, and from scipy import stats.

Mean, median, mode

st.mean(x)
st.median(x)
st.multimode(x)

Sample SD and variance

st.stdev(x)
st.variance(x)

Both divide by n − 1. Use st.pstdev for a population.

Correlation and covariance

np.corrcoef(x, y)[0, 1]
np.cov(x, y)[0, 1]

np.cov divides by n − 1 by default.

Combinations

import math
math.comb(5, 2)

Returns 10.

Binomial

stats.binom.pmf(2, 8, 0.2)
stats.binom.cdf(2, 8, 0.2)

Poisson

stats.poisson.pmf(3, 3)
stats.poisson.cdf(4, 6)

Normal areas and cutoffs

stats.norm.cdf(525, loc=400, scale=50)
stats.norm.ppf(0.9, loc=400, scale=50)

Critical values

stats.norm.ppf(0.975)
stats.t.ppf(0.975, 15)

CI for a mean from data

stats.t.interval(0.95, len(x) - 1, loc=np.mean(x), scale=stats.sem(x))

stats.sem is s / √n.

Regression

import statsmodels.formula.api as smf
fit = smf.ols("sales ~ adv", data=df).fit()
print(fit.summary())

df is a pandas DataFrame.

VIF

from statsmodels.stats.outliers_influence import variance_inflation_factor

Pass it the design matrix and a column index.