High School Statistics and Probability (Colorado Academic Standards)

Standard 3: Data, Statistics, and Probability

• MA.HS.S-ID.A Summarize, show and interpret data on one variable.
  • 1. Show data with dot plots, histograms and box plots on the real number line.
  • 2. Compare center (median, mean) and spread (IQR, standard deviation) of data sets using statistics suited to their shape.
  • 3. Interpret how data sets differ in shape, center and spread in context, allowing for outliers.
  • 4. Use mean and standard deviation to fit a normal distribution and estimate percentages, knowing when this is not appropriate.
• MA.HS.S-ID.B Summarize, show and interpret data on two variables. (being checked)
  • 1. Summarize two categorical variables in two-way tables and interpret joint, marginal and conditional relative frequencies.
  • 2. Make a scatter plot of two quantitative variables and describe how they are related.
  • 2.a. Fit a function (linear, quadratic or exponential) to data and use it to solve problems.
  • 2.b. Judge the fit of a function informally by plotting and analyzing residuals.
  • 2.c. Fit a line to a scatter plot that looks linear.
  • 3. Tell correlation apart from causation.
• MA.HS.S-ID.C Interpret linear models.
  • 1. Interpret the slope and intercept of a linear model in context.
  • 2. Use technology to find the correlation coefficient of a linear fit and interpret it.
• MA.HS.S-IC.A Understand random processes behind statistical experiments.
  • 1. Understand statistics as making inferences about a population from a random sample.
  • 2. Decide whether a model fits results from a data-generating process, e.g. by simulation.
• MA.HS.S-IC.B Draw and justify conclusions from surveys, experiments and observational studies.
  • 1. Know the purposes of sample surveys, experiments and observational studies and how randomization relates to each.
  • 2. Estimate a population mean or proportion from a sample survey and develop a margin of error by simulation.
  • 3. Compare two treatments in a randomized experiment and use simulation to judge significance.
  • 4. Evaluate reports based on data.
• MA.HS.S-CP.A Understand independence and conditional probability and use them with data.
  • 1. Describe events as subsets of the set of outcomes and with unions, intersections and complements ("or", "and", "not").
  • 2. Know events A and B are independent when P(A and B) = P(A) × P(B) and use this.
  • 3. Understand conditional probability P(A|B) = P(A and B)/P(B) and independence as P(A|B) = P(A).
  • 4. Build and read two-way tables to decide independence and find conditional probabilities.
  • 5. Explain conditional probability and independence in plain language with everyday examples.
• MA.HS.S-CP.B Use probability rules for compound events.
  • 1. Find P(A|B) as the share of B's outcomes that are also in A and interpret it.
  • 2. Apply the Addition Rule for "A or B" (add the two probabilities, subtract the overlap) and interpret it.
  • 3. (+) Use the general Multiplication Rule in a uniform model and interpret the result.
  • 4. (+) Use permutations and combinations to find probabilities of compound events.
• MA.HS.S-MD.A Find expected values and use them to solve problems.
  • 1. (+) Define a random variable for a quantity and graph its probability distribution.
  • 2. (+) Calculate a random variable's expected value as the mean of its distribution.
  • 3. (+) Build a theoretical probability distribution and find its expected value.
  • 4. (+) Build an empirical probability distribution and find its expected value.
• MA.HS.S-MD.B Use probability to evaluate decisions.
  • 1. (+) Weigh decision outcomes by assigning probabilities to payoffs and finding expected values.
  • 1.a. Find the expected payoff of a game of chance.
  • 1.b. Compare strategies using expected values (e.g. insurance choices).
  • 2. (+) Use probability to make fair decisions (drawing lots, random number generators).
  • 3. (+) Analyze decisions and strategies with probability (e.g. medical testing).