What does this Intro Statistics cheat sheet cover?

It has 10 sections: Descriptive Stats, Probability Rules, Counting & Random Variables, Binomial & Poisson, Normal & CLT, Confidence Intervals, Hypothesis Tests, Errors & t-tests, Chi-square Tests and Regression. Together they cover the topics a typical Intro Statistics exam tests, including descriptive statistics, probability rules and Bayes, binomial and Poisson and normal distribution and z-scores.

Is the statistics formula cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Intro Statistics cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 2 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Intro Statistics sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

MathIntro Statistics

Statistics Formula Cheat Sheet — 1-page PDF

Core formulas, tests, and rules for common exam problems. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

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For a specific exam: Intro Statistics Midterm study sheet, Intro Statistics Final exam study sheet.

1 pageUS Letter
10 sections11 topics
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Preview of the one-page Intro Statistics cheat sheet: Core formulas, tests, and rules for common exam problems — the whole course, one page

On the sheet

What’s on it

The topics a typical Intro Statistics exam tests, all on the one page.

Descriptive statistics
Probability rules and Bayes
Binomial and Poisson
Normal distribution and z-scores
Central limit theorem
Confidence intervals (mean, proportion)
Hypothesis testing and p-values
Type I/II errors
T-tests (one, two sample, paired)
Chi-square tests
Linear regression and correlation

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The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Descriptive Stats

Population mean: $μ = \frac{1}{N} \sum x_{i}$ ; average of all $N$ population values.
Sample mean: $\overset{x}{ˉ} = \frac{1}{n} \sum x_{i}$ ; average of $n$ sample values.

Sample variance

s^{2} = \frac{\sum ( x _{i} - x ˉ ) ^{2}}{n - 1}

unbiased for population variance $σ^{2}$ under SRS; $s = s^{2}$

Population variance

σ^{2} = \frac{\sum ( x _{i} - μ ) ^{2}}{N}

population version; $σ = σ^{2}$

z-score

z = \frac{x - μ}{σ} or z = \frac{x - x ˉ}{s}

standardized distance from mean

Center / spread

Measure	Symbol	Robust?
mean	$\overset{x}{ˉ}$	no
median	—	yes
SD	$s, σ$	no
IQR	$Q_{3} - Q_{1}$	yes

Watch out:Outliers pull $\overset{x}{ˉ}$ and $s$ ; use median/IQR for skewed data.

02Probability Rules

Independent: $A, B$ independent iff $P (A \cap B) = P (A) P (B)$ .

03Counting & Random Variables

Discrete vs continuous

Type	Probability	Area/point
discrete	$P (X = x)$	mass at points
continuous	$P (a \leq X \leq b)$	area under density

04Binomial & Poisson

Binomial model: $X \sim Bin (n, p)$ if: fixed $n$ , independent trials, two outcomes, constant $p$ .

Binomial pmf

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

$k = 0, 1, \dots, n$

Binomial mean/SD

μ = n p, σ = n p (1 - p)

for $X \sim Bin (n, p)$

Poisson model: $X \sim Pois (λ)$ counts events in fixed time/space with mean rate $λ$ .

Poisson pmf

P (X = k) = e^{- λ} \frac{λ ^{k}}{k !}

$k = 0, 1, 2, \dots$

Poisson mean/SD

μ = λ, σ = λ

for $X \sim Pois (λ)$

05Confidence Intervals

CI for proportion

\overset{p}{^} \pm z^{*} \frac{p ^ ( 1 - p ^ )}{n}

requires large-sample success/failure condition

CI for difference of means

(\overset{x}{ˉ}_{1} - \overset{x}{ˉ}_{2}) \pm t^{*} S E

use pooled or unpooled per course convention

CI for difference of proportions

(\overset{p}{^}_{1} - \overset{p}{^}_{2}) \pm z^{*} \frac{p ^ _{1} ( 1 - p ^ _{1} )}{n _{1}} + \frac{p ^ _{2} ( 1 - p ^ _{2} )}{n _{2}}

independent samples

Watch out:Interpretation: a $95%$ CI does not mean 95% probability parameter is in the interval; parameter fixed, interval random.

06Hypothesis Tests

Null / alternative: $H_{0}$ = default claim; $H_{a}$ = competing claim ( $<$ , $>$ , or $\neq =$ ).

Test statistic

test stat = \frac{estimate - null value}{S E}

compare to reference distribution

p-value: $P$ (test statistic as extreme or more extreme than observed, assuming $H_{0}$ true).

07Errors & t-tests

Watch out:Use $t$ methods for quantitative means when $σ$ unknown; use $z$ only for known $σ$ or proportions.

08Chi-square Tests

Expected count

E = \frac{( row total ) ( col total )}{grand total}

for contingency tables

Chi-square statistic

χ^{2} = \sum \frac{( O - E ) ^{2}}{E}

$O$ observed, $E$ expected

GOF df

df = k - 1 - m

$k$ categories, $m$ parameters estimated from data

Independence df

df = (r - 1) (c - 1)

$r \times c$ table

Chi-square uses

Test	$H_{0}$	Typical data
GOF	model fits	one categorical variable
Independence	variables independent	two-way table
Homogeneity	same distribution	multiple groups

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Also on the full Intro Statistics sheet

9 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Probability Rules

Complement
Addition rule
Conditional probability
Multiplication rule
Law of total probability
Bayes

Counting & Random Variables

Factorial
Combination
Permutation
Expected value
Variance of X

Binomial & Poisson

Normal & CLT

Normal distribution
Standardization
Percentile rule
68–95–99.7
Central Limit Theorem
Sampling mean

Confidence Intervals

Confidence interval
CI for mean (σ known)
CI for mean (σ unknown)

Hypothesis Tests

One-sided
Two-sided

Errors & t-tests

Type I error
Type II error
Power
Common t tests
Paired data
Equal-variance 2-sample SE

Chi-square Tests

Regression

Correlation
Least-squares line
Slope
Intercept
Residual
Coefficient of determination

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FAQ

Questions

About the Intro Statistics sheet and making your own.

What does this Intro Statistics cheat sheet cover?: It has 10 sections: Descriptive Stats, Probability Rules, Counting & Random Variables, Binomial & Poisson, Normal & CLT, Confidence Intervals, Hypothesis Tests, Errors & t-tests, Chi-square Tests and Regression. Together they cover the topics a typical Intro Statistics exam tests, including descriptive statistics, probability rules and Bayes, binomial and Poisson and normal distribution and z-scores.
Is the statistics formula cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Intro Statistics cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 2 statements before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Intro Statistics sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

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