Statistics

High school · Math

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1.1 — Displays of data. Create and interpret histograms, box plots, bar charts, and stem-and-leaf plots.
1.2 — Center and spread. Compute and interpret mean, median, IQR, and standard deviation.
1.3 — Describe skewness. Classify distributions as symmetric, left-skewed, or right-skewed and interpret their shape.
1.4 — Identify unusual points. Identify outliers, high-leverage points, and influential observations in bivariate data.

2.1 — Describe association. Describe the direction, form, and strength of association in bivariate data.
2.2 — Interpret correlation qualitatively. Interpret the direction and strength of correlation from scatterplots and context.
2.3 — Linear regression. Fit a least-squares line and interpret slope and intercept in context.
2.4 — Residuals. Use residual plots to assess linearity of a model.

3.1 — Use sample spaces and complements. Organize outcomes in sample spaces and use complements to calculate probabilities.
3.2 — Equally likely outcomes. Calculate probabilities by comparing favorable outcomes with equally likely outcomes.
3.3 — Compute conditional probabilities. Calculate conditional probabilities from tables, diagrams, or probability rules.
3.4 — Interpret independence. Interpret independence in context and explain how one event affects the probability of another.
3.5 — Apply permutations. Use permutations to count ordered arrangements in probability problems.
3.6 — Combinations in probability settings. Use combinations to count unordered selections in probability settings.

4.1 — Find expected value. Calculate and interpret the expected value of a discrete random variable.
4.2 — Variance for simple discrete distributions. Calculate and interpret the variance and standard deviation of simple discrete distributions.
4.3 — Identify binomial settings. Determine whether a probability setting satisfies the conditions for a binomial experiment.
4.4 — Compute binomial probabilities. Calculate probabilities for binomial random variables using the binomial probability formula.
4.5 — Use the empirical rule. Use the empirical rule to estimate proportions in approximately normal distributions.
4.6 — Z-scores for approximately normal data. Calculate and interpret z-scores for data from approximately normal distributions.

5.1 — Distinguish simple random, stratified, and cluster samples. Distinguish among simple random, stratified, and cluster sampling methods.
5.2 — Convenience samples. Identify convenience samples and explain how they may introduce bias.
5.3 — Identify sources of bias in surveys. Identify sources of sampling and response bias in surveys.
5.4 — Observational studies. Explain what observational studies can reveal and why they cannot establish causation.
5.5 — Describe randomization and control. Explain how randomization and control help produce valid experimental conclusions.
5.6 — Replication in experiments. Explain how replication reduces variability and strengthens evidence in experiments.

6.1 — Sampling distributions (intro). Describe the sampling distribution of a sample mean or proportion conceptually.
6.2 — Confidence intervals (intro). Interpret a basic confidence interval for a proportion or mean.
6.3 — State hypotheses. State appropriate null and alternative hypotheses for a statistical test.
6.4 — Interpret p-values at an introductory level. Interpret a p-value as evidence against a null hypothesis at an introductory level.