Probability and Statistics

Link to the Probability and Statistics curriculum map

On a day-to-day basis, our Probability and Statistics courses may be the most practical of our high school math classes. We are all routinely expected to live in a world of uncertainty: to interpret the results of surveys, describe and understand what it means for something to be "typical", draw conclusions about a group based on information about a few individuals, decide whether an outcome is common or rare, determine whether information was gathered in an unbiased way, and so on. All of these are questions are informed by probability and statistics. This particular course is primarily taken by students with an interest in probability and statistics who prefer not to take the more rigorous AP version of the class, or by students who have chosen not to take Pre-calculus and are in need of a required fourth high school math credit.

The course is broadly divided into thirds, with one third focused on descriptive statistics, one third on probability, and one third on inferential statistics. It proceeds at a relatively measured pace with the great majority of work being done in the classroom. Students routinely gather and analyze their own data through surveys, experiments, and simulations. They work both individually and in small groups for assignments and on assessments. Exercises build on students' skills in Algebra with an emphasis on justifying and clearly communicating results using mathematical language. Few formulas must be memorized, but many must be correctly applied to solve the problems presented.

Key elements taught in the course include:

• Analyzing and displaying one variable data
  • Measures of center and spread, five number summaries, outliers, graphical depictions of data
• Analyzing two-variable data
  • Scatterplots, correlation, regression, prediction, residuals
• Sampling and experiments
  • Sampling methods, bias, experimental design
• Probability
  • Independent and dependent events, addition and multiplication rules, conditional probabilities, expected value, binomial events, combinatorics
• Sampling distributions and the normal distribution
  • The empirical rule, z-scores
• Confidence intervals
  • Margins of error, confidence intervals for population proportions and means, t statistics
• Significance and hypothesis testing
  • Type I and Type II errors, null and alternative hypotheses, p values, one- and two-sided tests, significance and hypothesis tests for proportions, means, and paired data
• Comparing two samples
  • Confidence intervals and hypothesis tests for the difference between sample means and proportions
• Categorical data
  • Chi-squared tests for independence and goodness of fit