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Informational

Statistics formulas cheat sheet

The expressions below are the ones intro statistics courses use constantly. Use them to set up homework; use a calculator or a step-by-step solver to check the arithmetic. This is not every formula in statistics — it is the core set that matches what Statistics Problem Solver Pro lists on the App Store.

Descriptive statistics

Mean: x̄ = Σxᵢ / n
Sample variance: s² = Σ(xᵢ − x̄)² / (n − 1)
Sample SD: s = √s²
Population SD: σ = √[ Σ(xᵢ − μ)² / n ]

Median and mode do not have a single algebraic line — they are rules on the ordered list. Walkthrough: mean, median, and mode · standard deviation.

Standardizing and the normal curve

z = (x − μ) / σ
z for a mean: (x̄ − μ) / (σ / √n)

Normal CDF turns a z into a left-tail probability. The app’s visualizer shades Normal and Binomial regions. Walkthrough: z-score.

Inference for a mean

t = (x̄ − μ0) / (s / √n), df = n − 1
CI (known σ): x̄ ± z* · (σ / √n)
CI (unknown σ): x̄ ± t* · (s / √n)

Walkthroughs: t-test · confidence interval.

Association

Pearson r measures linear association between two quantitative variables (between −1 and 1).
Simple linear regression: ŷ = a + bx (slope and intercept estimated from the paired data).

The app includes Correlation (Pearson r) and Linear Regression calculators. Interpretation still belongs to you: r does not prove causation.

Probability snapshots

Binomial P(X = k) = C(n, k) p^k (1 − p)^{n − k}

Normal CDF is the continuous counterpart for a specified mean and SD. Both appear in the free calculator list.

In-app statistics formula reference grouped by descriptive, probability, inference, and regression

How to use this sheet on homework

  1. Name the procedure from the question stem.
  2. Copy only that formula onto your paper.
  3. Substitute, then compute.
  4. If the algebra is the blocker, check with the matching iPhone calculator or scan the problem.

Useful tips

  • Write σ vs s every time. Mixing them is the most common formula error in inference.
  • The in-app reference is searchable and grouped by topic — closer to a pocket card than this page, and it stays free.
  • Flashcards from a solved problem (v2.0) are for remembering which formula you just used, not for inventing a new one.

Common mistakes

  • Memorizing symbols without the conditions (known σ, sample size, paired vs two-sample).
  • Using the binomial formula on data that are not n independent Bernoulli trials.
  • Treating this page as a substitute for your course’s allowed formula sheet on an exam.

How Statistics Problem Solver Pro helps

The App Store description includes a searchable formula reference grouped by topic, with the exact formula for each concept. Combined with offline calculators, you can look up the expression and evaluate it without using an AI solve.

Keep the formulas on your iPhone

Download Statistics Problem Solver Pro — the formula reference is always free.

Download on the App Store

Related guides

Statistics calculator for iPhone How to calculate a z-score How to calculate a confidence interval

FAQ

Is this the same as the in-app formula reference?

This page is a short public cheat sheet. The app’s reference is searchable, grouped by topic, and includes more entries (the listing screenshot describes dozens of formulas). Use the app when you need the full list on a phone.

See the formula reference screenshot →
Do I need Pro to open formulas?

No. The listing says the formula reference is always free, along with the calculators and visualizer.

Download the app →

Statistics Problem Solver Formula reference

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