Probability & statistics cheat sheet

Descriptive statistics summarise data you already have; probability describes data you might get. Keep the two sets of formulas mentally separate and the notation stops being confusing.

Practise statistics & probability

Descriptive

$x ˉ = \frac{\sum x _{i}}{n}$
$s^{2} = \frac{\sum ( x _{i} - x ˉ ) ^{2}}{n - 1}$ Sample variance
$σ^{2} = \frac{\sum ( x _{i} - μ ) ^{2}}{N}$ Population variance
$IQR = Q_{3} - Q_{1}$
$C V = \frac{s}{x ˉ} \cdot 100%$

Probability rules

$P (A^{'}) = 1 - P (A)$
$P (A \cup B) = P (A) + P (B) - P (A \cap B)$
$P (A \cap B) = P (A) P (B ∣ A)$
$P (B ∣ A) = \frac{P ( A ∣ B ) P ( B )}{P ( A )}$ Bayes

Counting

$n!$
$^{n} P_{r} = \frac{n !}{( n - r )!}$
$^{n} C_{r} = \frac{n !}{r ! ( n - r )!}$

Distributions & inference

$P (X = k) =^{n} C_{k} p^{k} (1 - p)^{n - k}$ Binomial
$μ = n p, σ = n p (1 - p)$
$z = \frac{x - μ}{σ}$
$x ˉ \pm z^{*} \frac{s}{n}$ Confidence interval

Related calculators

Standard Deviation Probability Calculator