Statistics symbols and what they mean
The notation used in statistics, grouped so the pairs that get mixed up sit next to each other. The single most important distinction is sample vs population: Latin letters (x̄, s, p̂) describe the sample you collected, Greek letters (μ, σ, ρ) describe the population you are trying to learn about. Click any symbol with a link to copy it and see how to type it.
Also known as: statistics symbols, stats symbols, stat symbols, symbols in statistics, statistical symbols, statistics symbols and meanings, statistics symbols cheat sheet, symbols of probability.
29 symbols, 17 with a full copy-and-type guide.
Sample vs population — the distinction everything rests on
| x̄ | Sample mean — the average of the data you actually collected. How to type x̄ → | |
| μ | Population mean — the true average of the whole population, usually unknown. How to type μ → | |
| s | Sample standard deviation. Divides by n − 1, not n, to stay unbiased. | |
| σ | Population standard deviation. How to type σ → | |
| s² | Sample variance — the square of s. | |
| σ² | Population variance — the square of σ. | |
| p̂ | Sample proportion — read “p-hat”. The share of the sample with the trait. How to type p̂ → | |
| p | Population proportion. | |
| n | Sample size — how many observations you have. | |
| N | Population size. |
Spread, shape and relationship
| ρ | Population correlation coefficient (rho) — the true linear association. How to type ρ → | |
| r | Sample correlation coefficient, the estimate of ρ. | |
| χ² | Chi-squared statistic, used for goodness-of-fit and independence tests. How to type χ² → | |
| z | z-score — how many standard deviations from the mean. | |
| t | t-statistic, used when σ is unknown and n is small. | |
| λ | Rate parameter of the Poisson and exponential distributions. How to type λ → |
Hypothesis testing and regression
| H₀ | Null hypothesis — the claim you test against. Read “H-naught”. How to type H₀ → | |
| H₁ | Alternative hypothesis (also written Hₐ). | |
| α | Significance level — the Type I error rate you accept, commonly 0.05. How to type α → | |
| β | Type II error rate; 1 − β is the power of the test. | |
| ŷ | Predicted value from a regression — read “y-hat”. How to type ŷ → | |
| ν | Degrees of freedom (also written df). |
Operators you will meet in statistics formulas
| Σ | Summation — add up the terms that follow. How to type Σ → | |
| ∏ | Product — multiply the terms. Used for likelihoods of independent events. How to type ∏ → | |
| | | “Given” — P(A | B) is the probability of A given that B happened. How to type | → | |
| ∈ | Is an element of — x ∈ S means x is in the set S. How to type ∈ → | |
| ≈ | Approximately equal to. How to type ≈ → | |
| ± | Plus or minus — used for margins of error and confidence intervals. How to type ± → | |
| ∝ | Is proportional to. How to type ∝ → |