Statistics Tables
Every distribution table a statistics course actually uses, in one place: the z table, the t distribution table, the chi square table, the f distribution table and the binomial table — every value generated from the distribution itself and anchor-checked against published tables.
The tables
Z Score Table
The standard normal table: cumulative areas for z from −3.99 to 3.99, with the interactive finder, in three layouts.
T Distribution Table
Critical t values by degrees of freedom — the table for inference when σ is unknown and samples are small.
Chi Square Table
Right-tail critical values for goodness-of-fit, independence and variance tests.
F Distribution Table
Critical F values at α = 0.05 and 0.01 for ANOVA and variance-ratio tests, by both degrees of freedom.
Binomial Distribution Table
Cumulative probabilities P(X ≤ x) for n = 5, 10, 15 and 20 trials across success probabilities.
Custom Z Table Generator
Build a z table to your own range, step and layout, and download it as CSV or PNG.
Which table do I need?
If you are unsure where to start, begin with the question your statistic answers, then choose the table whose distribution matches that statistic — the five routes below cover the standard cases.
- Normal data, known σ, or large samples: the z table. Probabilities and percentiles for standardised values.
- Means with unknown σ, small samples: the t table, entered with degrees of freedom n − 1. The z table vs t table page gives the full decision rules.
- Counts in categories, or testing a variance: the chi-square table — always a right-tail lookup.
- Comparing two or more group variances (ANOVA): the f table, entered with numerator and denominator degrees of freedom.
- Successes in a fixed number of trials: the binomial table, entered with n and p.
Students meeting these tables for the first time often ask which of them "is" a probability distribution table — all of them are, each for its own distribution; the blog post which table is a probability distribution table? explains how to tell them apart on sight.
How these values are made — and checked
Most table sites photograph or transcribe printed tables, inheriting every typo those printings ever contained. Here, each value is computed at build time from its distribution's cumulative function — the same mathematics statistical software uses — and then spot-checked against the anchors printed tables are famous for: t(0.975, df 10) = 2.228, χ²(0.95, df 10) = 18.307, F(0.95; 2, 10) = 4.10, P(X ≤ 2) for n = 10, p = 0.5 is 0.0547. If a value on this site disagrees with your textbook, the likeliest cause is rounding (our cells carry more precision than most printings) — and the contact line below exists for the other cases.
Frequently asked questions
Why are there different tables for different tests?
Because each test statistic follows its own distribution. A standardised mean with known σ follows the normal (z) distribution; with estimated σ it follows t; squared standard normals summed give chi-square; ratios of variances give F; counts of successes give the binomial. The table must match the statistic's distribution or the probabilities are wrong.
Can I print or download these tables?
Yes. Every table page prints cleanly (use your browser's print command — the navigation and tools hide themselves), the z table additionally offers finished PDF, CSV and PNG downloads, and the custom generator exports any z range you specify.
What are degrees of freedom, in one sentence?
The number of independent pieces of information available to estimate variability — for a single sample, n − 1, because the sample mean itself consumes one. It is the entry key for the t, chi-square and F tables.