Statistics and Probability (Iowa Core)

Statistics and Probability (S)

• ST.S-ID.A.1 Show data on a number line with dot plots, histograms and box plots.
• ST.S-ID.A.2 Compare center and spread of two or more data sets with statistics suited to their shape.
• ST.S-ID.A.3 Explain in context how data sets differ in shape, center and spread, allowing for outliers.
• ST.S-ID.A.4 Fit data to a normal curve with mean and standard deviation to estimate percentages, knowing when not to.
• ST.S-ID.B.5 Summarize two categorical variables in two-way tables and interpret joint, marginal and conditional relative frequencies.
• ST.S-ID.B.6 Show two quantitative variables on a scatter plot, fit functions, check residuals and fit lines to linear trends.
• ST.S-ID.C.7 Explain what a linear model's slope and intercept mean for the data.
• ST.S-ID.C.8 Use technology to find and interpret the correlation coefficient of a linear fit.
• ST.S-ID.C.9 Tell correlation apart from causation.
• ST.S-IC.A.1 See statistics as a process for inferring population parameters from a random sample.
• ST.S-IC.A.2 Judge whether a model fits results from a data-generating process, e.g. using simulation.
• ST.S-IC.B.3 Tell apart sample surveys, experiments and observational studies and explain the role of randomization in each.
• ST.S-IC.B.4 Estimate a population mean or proportion from a survey and build a margin of error by simulation.
• ST.S-IC.B.5 Compare two treatments in a randomized experiment and use simulation to judge whether differences are significant.
• ST.S-IC.B.6 Critically evaluate reports and claims that rest on data.
• ST.S-IC.IA.B.1 Carry out statistical investigations, both observational studies and experiments (a–b).
• ST.S-CP.A.1 Describe events as parts of a sample space or as unions, intersections or complements of events.
• ST.S-CP.A.2 Understand that A and B are independent when the probability of both is the product of their probabilities, and use this.
• ST.S-CP.A.3 Understand conditional probability of A given B and interpret independence in terms of it.
• ST.S-CP.A.4 Build and interpret two-way frequency tables and use them to judge independence and estimate conditional probabilities.
• ST.S-CP.A.5 Explain conditional probability and independence in everyday language and situations.
• ST.S-CP.B.6 Find P(A given B) as the fraction of B's outcomes that are also in A and interpret it.
• ST.S-CP.B.7 Apply the addition rule for A or B (add both, subtract the overlap) and interpret it.
• ST.S-CP.B.8 Use the general multiplication rule in a uniform model and interpret the result.
• ST.S-CP.B.9 Compute probabilities of compound events with permutations and combinations.
• ST.S-MD.A.1 Define a random variable by giving each outcome a number and graph its probability distribution.
• ST.S-MD.A.2 Find the expected value of a random variable and read it as the distribution's mean.
• ST.S-MD.A.3 Build a probability distribution from theoretical probabilities and find its expected value.
• ST.S-MD.A.4 Build a probability distribution from empirical probabilities and find its expected value.
• ST.S-MD.B.5 Weigh decisions by attaching probabilities to payoffs and finding expected values, e.g. games or insurance (a–b).
• ST.S-MD.B.6 Use probability to make fair decisions, e.g. drawing lots or random number generators.
• ST.S-MD.B.7 Analyze decisions and strategies using probability, e.g. product or medical testing.
• ST.N-APR.C.5 Know and use the Binomial Theorem to expand (x + y) to the n, with coefficients from Pascal's triangle.