Statistics and Probability Flashcards
Free statistics and probability flashcards for descriptive statistics, probability rules, counting, the normal distribution, z-scores and the basics of inference. Flip each card, mark what you know and drill what you miss.
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Descriptive statistics
| Question | Answer |
|---|---|
| Mean? | The sum of the values divided by how many there are. |
| Median? | The middle value of the sorted data (average the two middle values if the count is even). |
| Mode? | The value that appears most often. |
| Range? | Maximum minus minimum. |
| Interquartile range (IQR)? | Q3 − Q1 |
| How do you find outliers with the 1.5 × IQR rule? | Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. |
| Population variance? | σ² = Σ(x − μ)² / N |
| Sample variance? | s² = Σ(x − x̄)² / (n − 1) |
| Standard deviation? | The square root of the variance. |
| Which measure of center resists outliers? | The median. |
| What does a right-skewed distribution look like? | A long tail to the right, with the mean greater than the median. |
Probability basics
| Question | Answer |
|---|---|
| Probability of an event? | P(A) = favorable outcomes / total equally likely outcomes |
| What values can a probability take? | Between 0 and 1, inclusive. |
| Complement rule? | P(not A) = 1 − P(A) |
| Addition rule? | P(A or B) = P(A) + P(B) − P(A and B) |
| Mutually exclusive events? | Events that cannot both happen, so P(A and B) = 0. |
| Multiplication rule for independent events? | P(A and B) = P(A) × P(B) |
| Conditional probability? | P(A | B) = P(A and B) / P(B) |
| General multiplication rule? | P(A and B) = P(A) × P(B | A) |
| When are A and B independent? | When P(A | B) = P(A). |
| Bayes’ theorem? | P(A | B) = P(B | A) P(A) / P(B) |
| Expected value of a discrete variable? | E(X) = Σ x · P(x) |
Counting
| Question | Answer |
|---|---|
| Factorial n!? | n × (n − 1) × … × 1, with 0! = 1. |
| Permutations of r items from n? | nPr = n! / (n − r)! |
| Combinations of r items from n? | nCr = n! / [r!(n − r)!] |
| When do you use a permutation? | When order matters. |
| When do you use a combination? | When order does not matter. |
| Compute 5C2. | 10 |
| Compute 5P2. | 20 |
| Compute 6!. | 720 |
| Fundamental counting principle? | Multiply the number of choices at each step. |
Normal distribution and z-scores
| Question | Answer |
|---|---|
| z-score formula? | z = (x − μ) / σ |
| Empirical rule (68-95-99.7)? | About 68% of data lies within 1 SD of the mean, 95% within 2 SDs, 99.7% within 3 SDs. |
| What are the mean and SD of the standard normal distribution? | Mean 0, standard deviation 1. |
| What percentile is a z-score of 0? | The 50th percentile. |
| z-score of 2 is roughly which percentile? | About the 97.7th percentile. |
| What does a negative z-score mean? | The value is below the mean. |
| Central Limit Theorem? | For large samples, the distribution of the sample mean is approximately normal, with mean μ and standard deviation σ/√n. |
| Standard error of a sample mean? | σ / √n (or s / √n) |
Distributions and inference
| Question | Answer |
|---|---|
| Binomial probability? | P(X = k) = nCk · pᵏ · (1 − p)ⁿ⁻ᵏ |
| Mean and SD of a binomial variable? | Mean np; standard deviation √[np(1 − p)] |
| What is a confidence interval? | A range of plausible values for a population parameter, built from sample data. |
| General form of a confidence interval? | estimate ± (critical value) × (standard error) |
| What is a null hypothesis? | The default claim of no effect or no difference that a test tries to find evidence against. |
| What does a p-value measure? | The probability of results at least as extreme as observed, assuming the null hypothesis is true. |
| What is a Type I error? | Rejecting a true null hypothesis (a false positive). |
| What is a Type II error? | Failing to reject a false null hypothesis (a false negative). |
| Correlation coefficient r ranges from? | −1 to 1. |
| Does correlation imply causation? | No. A relationship can come from a lurking variable or chance. |
Frequently asked questions
What is the difference between population and sample standard deviation?
The sample version divides by n − 1 instead of N, which corrects for the sample underestimating spread in the population.
When should I use a permutation instead of a combination?
Use a permutation when order matters, such as arranging people in a line, and a combination when it does not, such as choosing a committee.
Do these cards cover the AP Statistics exam?
They cover core terms and formulas. AP Statistics also tests interpretation in context, so practice writing full conclusions.
Sources
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