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### Exploring Data

- S.ID Interpreting Categorical and Quantitative Data
- S.ID.A Understand, represent, and use univariate data.
- S.ID.A.1 Understand the term ‘variable’ and differentiate between the data types: measurement, categorical, univariate, and bivariate.
- S.ID.A.2 Understand histograms, parallel box plots, and scatterplots, and use them to display and compare data.
- S.ID.A.3 Summarize distributions of univariate data.
- S.ID.A.4 Compute basic statistics and understand the distinction between a statistic and a parameter.
- S.ID.A.5 For univariate measurement data, be able to display the distribution and describe its shape; select and calculate summary statistics.
- S.ID.A.6 Recognize how linear transformations of univariate data affect shape, center, and spread.
- S.ID.A.7 Analyze the effect of changing units on summary measures.
- S.ID.A.8 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
- S.ID.A.9 Describe individual performances in terms of percentiles, z-scores, and t-scores.

- S.ID.B Understand, represent, and use bivariate data.
- S.ID.B.10 Represent and analyze categorical data.
- S.ID.B.11 Display and discuss bivariate data where at least one variable is categorical.
- S.ID.B.12 For bivariate measurement data, be able to display a scatterplot and describe its shape; use technological tools to determine regression equations and correlation coefficients.
- S.ID.B.13 Identify trends in bivariate data; find functions that model the data and that transform the data so that they can bemodeled.

- S.ID.A Understand, represent, and use univariate data.

### Probability

- S.CP Conditional Probability and the Rules of Probability
- S.CP.A Understand and apply basic concepts of probability.
- S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
- S.CP.A.2 Use permutations and combinations to compute probabilities of compound events and solve problems.
- S.CP.A.3 Demonstrate an understanding of the Law of Large Numbers (Strong and Weak).

- S.CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model.
- S.CP.B.4 Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence.
- S.CP.B.5 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

- S.CP.A Understand and apply basic concepts of probability.

### Probability Distributions

- S.MD Using Probability to Make Decisions
- S.MD.A Understand and use discrete probability distributions.
- S.MD.A.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
- S.MD.A.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
- S.MD.A.3 Design a simulation of random behavior and probability distributions (e.g., drawing by lots, using a random number generator, and using the results to make fair decisions).
- S.MD.A.4 Analyze discrete random variables and their probability distributions, including binomial and geometric.
- S.MD.A.5 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
- S.MD.A.6 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
- S.MD.A.7 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
- S.MD.A.7.a Find the expected payoff for a game of chance.
- S.MD.A.7.b Evaluate and compare strategies on the basis of expected values.

- S.MD.A.8 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

- S.MD.B Understand the normal probability distribution.
- S.MD.B.9 Calculate the mean (expected value) and standard deviation of both a random variable and a linear transformation of a random variable.
- S.MD.B.10 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

- S.MD.A Understand and use discrete probability distributions.

### Sampling and Experimentation

- S.IC Making Inferences and Justifying Conclusions
- S.IC.A Know the characteristics of well-designed studies.
- S.IC.A.1 Understand the differences among various kinds of studies and which types of inferences can be legitimately drawn from each.
- S.IC.A.2 Compare census, sample survey, experiment, and observational study.
- S.IC.A.3 Describe the role of randomization in surveys and experiments.
- S.IC.A.4 Describe the role of experimental control and its effect on confounding.
- S.IC.A.5 Identify bias in sampling and determine ways to reduce it to improve results.
- S.IC.A.6 Describe the sampling distribution of a statistic and define the standard error of a statistic.
- S.IC.A.7 Demonstrate an understanding of the Central Limit Theorem.

- S.IC.B Design and conduct a statistical experiment to study a problem, then interpret and communicate the outcomes.
- S.IC.B.8 Select a method to collect data and plan and conduct surveys and experiments.
- S.IC.B.9 Compare and use sampling methods, including simple random sampling, stratified random sampling, and cluster sampling.
- S.IC.B.10 Test hypotheses using appropriate statistics.
- S.IC.B.11 Analyze results and make conclusions from observational studies, experiments, and surveys.
- S.IC.B.12 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

- S.IC.C Make inferences about population parameters based on a random sample from that population.
- S.IC.C.13 Develop and evaluate inferences and predictions that are based on data.
- S.IC.C.14 Use properties of point estimators, including biased/unbiased, and variability.

- S.IC.D Understand and use confidence intervals.
- S.IC.D.15 Understand the meaning of confidence level, of confidence intervals, and the properties of confidence intervals.
- S.IC.D.16 Construct and interpret a large sample confidence interval for a proportion and for a difference between two proportions.
- S.IC.D.17 Construct the confidence interval for a mean and for a difference between two means.

- S.IC.E Use distributions to make inferences about a data set.
- S.IC.E.18 Apply the properties of a Chi-square distribution in appropriate situations in order to make inferences about a data set.
- S.IC.E.19 Apply the properties of the normal distribution in appropriate situations in order to make inferences about a data set.
- S.IC.E.20 Interpret the t-distribution and determine the appropriate degrees of freedom.

- S.IC.A Know the characteristics of well-designed studies.