High School Statistics and Probability (Alaska Standards)

Interpreting Categorical & Quantitative Data

• S-ID.1 Show data with dot plots, histograms and box plots on the real number line.
• S-ID.2 Compare center (median, mean) and spread (IQR, standard deviation) of data sets using statistics suited to their shape.
• S-ID.3 Interpret how data sets differ in shape, center and spread in context, allowing for outliers.
• S-ID.4 Use mean and standard deviation to fit a normal distribution and estimate percentages, knowing when this is not appropriate.
• S-ID.5 Summarize two categorical variables in two-way tables and interpret joint, marginal and conditional relative frequencies.
• S-ID.6 Make a scatter plot of two quantitative variables and describe how they are related.
• S-ID.7 Interpret the slope and intercept of a linear model in context.
• S-ID.8 Use technology to find the correlation coefficient of a linear fit and interpret it.
• S-ID.9 Tell correlation apart from causation.

Making Inferences & Justifying Conclusions

• S-IC.1 Understand statistics as making inferences about a population from a random sample.
• S-IC.2 Decide whether a model fits results from a data-generating process, e.g. by simulation.
• S-IC.3 Know the purposes of sample surveys, experiments and observational studies and how randomization relates to each.
• S-IC.4 Estimate a population mean or proportion from a sample survey and develop a margin of error by simulation.
• S-IC.5 Compare two treatments in a randomized experiment and use simulation to judge significance.
• S-IC.6 Evaluate reports based on data.

Conditional Probability & the Rules of Probability

• S-CP.1 Describe events as subsets of the set of outcomes and with unions, intersections and complements ("or", "and", "not").
• S-CP.2 Know events A and B are independent when P(A and B) = P(A) × P(B) and use this.
• S-CP.3 Understand conditional probability P(A|B) = P(A and B)/P(B) and independence as P(A|B) = P(A).
• S-CP.4 Build and read two-way tables to decide independence and find conditional probabilities.
• S-CP.5 Explain conditional probability and independence in plain language with everyday examples.
• S-CP.6 Find P(A|B) as the share of B's outcomes that are also in A and interpret it.
• S-CP.7 Apply the Addition Rule for "A or B" (add the two probabilities, subtract the overlap) and interpret it.
• S-CP.8 (+) Use the general Multiplication Rule in a uniform model and interpret the result.
• S-CP.9 (+) Use permutations and combinations to find probabilities of compound events.

Using Probability to Make Decisions

• S-MD.1 (+) Define a random variable for a quantity and graph its probability distribution.
• S-MD.2 (+) Calculate a random variable's expected value as the mean of its distribution.
• S-MD.3 (+) Build a theoretical probability distribution and find its expected value.
• S-MD.4 (+) Build an empirical probability distribution and find its expected value.
• S-MD.5 (+) Weigh decision outcomes by assigning probabilities to payoffs and finding expected values.
• S-MD.6 (+) Use probability to make fair decisions (drawing lots, random number generators).
• S-MD.7 (+) Analyze decisions and strategies with probability (e.g. medical testing).