How to use this statistics deck

Statistics flashcards work best when each card tests one decision, definition or formula—not a whole topic at once. This deck covers ideas that recur across introductory statistics courses: descriptive measures, probability distributions, estimation, hypothesis testing and simple linear regression. Your course may use different notation, so match symbols and assumptions to your own notes.

Work through the cards in order. For each one, read the question, say or write a complete answer, then reveal the answer and compare it with yours. Grade your recall using the four buttons in the study interface: choose the grade that reflects how readily and correctly you answered, not how familiar the formula looks. A correct answer reached only after a long struggle needs more review than one recalled promptly.

The first card is face-up to show how a single fact is tested. The remaining cards are queued beneath it; answer each before revealing it, then grade your recall. In MySummaries, a statistics board can turn your own course notes into a deck like this:

Cards — Statistics foundations18 due

What is the sample mean for observations x₁, …, xₙ?

x̄ = (Σxᵢ)/n: add the observations and divide by n.

All 18 cards
What is the sample mean for observations x₁, …, xₙ?x̄ = (Σxᵢ)/n: add the observations and divide by n.
Which measure of centre is resistant to extreme observations?The median; it is the middle ordered value, or the mean of the two middle values when n is even.
How is the interquartile range defined?IQR = Q₃ − Q₁, the difference between the third and first quartiles.
What is the sample variance s² for n observations?s² = Σ(xᵢ − x̄)²/(n − 1); the deviations are squared and divided by n − 1.
What are the units of a standard deviation?The same units as the original observations; variance has squared units.
What is the standard error of the sample mean when population SD σ is known?SE(x̄) = σ/√n, for independent observations with finite variance.
What is the usual estimated standard error of the sample mean when σ is unknown?SE(x̄) = s/√n, using the sample standard deviation s.
What does a 95% confidence procedure mean in repeated sampling?If its assumptions hold, 95% of intervals produced by the procedure over repeated samples would contain the fixed population parameter.
What is the z-score of an observation x from a normal distribution with mean μ and SD σ?z = (x − μ)/σ; it gives the distance from μ in standard deviation units.
What is the probability mass function of X ~ Binomial(n, p)?P(X = k) = C(n,k)pᵏ(1 − p)ⁿ⁻ᵏ, for k = 0, …, n.
What is the expected value of X ~ Binomial(n, p)?E(X) = np.
What is the variance of X ~ Binomial(n, p)?Var(X) = np(1 − p).
What is the null hypothesis in a significance test?The specified reference claim about a population parameter or data-generating process, assessed using a test statistic under that claim.
What does a p-value measure?Assuming the null hypothesis and model are true, it is the probability of a result at least as extreme as the observed result, in the direction defined by the test.
What is a Type I error?Rejecting a true null hypothesis; the test's significance level α is its long-run Type I error probability under the specified conditions.
What is the power of a test at a particular alternative?The probability of rejecting the null hypothesis when that alternative is true; power = 1 − β, where β is the Type II error probability.
What does the slope β₁ mean in the simple linear regression model E(Y|X) = β₀ + β₁X?The change in the modelled mean of Y for a one-unit increase in X.
What does a correlation of r = 0 establish?It establishes no linear association in the sample; it does not rule out a nonlinear relationship.

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Check the ideas behind the formulas

Once you have graded all 18 cards, identify whether any wrong answers came from confusing a definition with an interpretation. A formula recalled without its conditions can still lead to a wrong conclusion. For instance, the standard error describes the variability of a statistic across samples; it is not the spread of individual observations. The sample standard deviation describes the latter, while the standard error of the mean estimates how much sample means vary.

The confidence-interval card is another common source of imprecise wording. In the frequentist interpretation, the population parameter is fixed and the interval varies from sample to sample. Avoid saying that there is a 95% probability the fixed parameter lies in this particular interval. If your course teaches a different inferential framework, follow its definitions and distinguish it explicitly.

For hypothesis testing, keep the p-value tied to the null model: it is not the probability that the null hypothesis is true, nor the probability that the result happened “by chance”. A small p-value can be evidence against the null under the stated model, but it does not measure the size or practical importance of an effect. Report an effect estimate and uncertainty as well when the question or course requires them.

Build a compact core checklist

After grading, reduce the deck to a few facts you must be able to retrieve without hesitation. This is not a replacement for working through the cards: it is a quick self-check before a practice problem. In MySummaries, the deck’s core checklist can look like this:

Must not miss coreStatistics foundations
Sample variance: s² = Σ(xᵢ − x̄)²/(n − 1); sample SD is √s² and has the data's units.
Mean standard error: σ/√n when σ is known, or estimated by s/√n when it is unknown, under independent sampling with finite variance.
Binomial model: n fixed independent Bernoulli trials with common success probability p; E(X) = np and Var(X) = np(1 − p).
A p-value is calculated assuming the null and model; it is not the probability that the null is true.
Simple regression slope: expected change in mean Y for one-unit higher X; correlation describes linear association, not causation.

Turn missed marks into another card

Do not respond to a difficult card by rereading the whole chapter straight away. First locate the exact gap: was the formula wrong, was a condition missing, or was the interpretation inaccurate? Then return to your course material and correct that point. A useful follow-up card asks for the distinction you missed, rather than repeating the original wording.

For example, if you twice describe a p-value as the probability that the null is true, the repair card should make you state the conditioning assumption and the event being measured. In MySummaries, a repeated missed mark can appear in a remediation tray as a short prompt to revisit:

Remediation tray

You lost this mark twice: under the null hypothesis and the stated model, what probability does a p-value represent—and what probability does it not represent?

Add cardDismiss

Make the deck fit your course

This is a foundations deck, not a complete statistics syllabus. Add cards from your own notes for topics your course assesses, such as sampling distributions, tests for means or proportions, analysis of variance, contingency tables, Bayesian methods or the assumptions of a particular regression model. Keep one card to one retrievable answer. If a card requires a paragraph, split it into a definition, a condition and an interpretation.

After a practice question, turn each lost mark into a precise prompt. “Review regression” is too broad; “What does the intercept represent when X = 0, and when is that interpretation meaningful?” gives you something answerable. Keep a separate card for assumptions if they are easy to omit, and practise applying the method to a small numerical example as well as recalling the formula.

How MySummaries helps

MySummaries builds revision boards from your PDFs, slides and photographed notes, then generates flashcards from those materials. You can use a board to keep formulas, assumptions and interpretations together, and practise the resulting cards with spaced repetition. Start at portal.mysummaries.app.