### AR.Math.Content.HSS.ID: Interpreting Categorical and Quantitative Data

#### AR.Math.Content.HSS.ID.A: Summarize, represent, and interpret data on a single count or measurement variable

AR.Math.Content.HSS.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

AR.Math.Content.HSS.ID.A.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

AR.Math.Content.HSS.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

AR.Math.Content.HSS.ID.A.4: 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 and/or spreadsheets to estimate areas under the normal curve.

#### AR.Math.Content.HSS.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables

AR.Math.Content.HSS.ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Informally assess the fit of a function by plotting and analyzing residuals.

#### AR.Math.Content.HSS.ID.C: Interpret linear models

AR.Math.Content.HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

AR.Math.Content.HSS.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.

### AR.Math.Content.HSS.IC: Making Inferences and Justifying Conclusions

#### AR.Math.Content.HSS.IC.A: Understand and evaluate random processes underlying statistical experiments

AR.Math.Content.HSS.IC.A.1: Recognize statistics as a process for making inferences about population parameters based on a random sample from that population.

AR.Math.Content.HSS.IC.A.2: Compare theoretical and empirical probabilities using simulations (e.g. such as flipping a coin, rolling a number cube, spinning a spinner, and technology).

#### AR.Math.Content.HSS.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

AR.Math.Content.HSS.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies. Explain how randomization relates to sample surveys, experiments, and observational studies.

AR.Math.Content.HSS.IC.B.4: Use data from a sample survey to estimate a population mean or proportion. Develop a margin of error through the use of simulation models for random sampling.

AR.Math.Content.HSS.IC.B.5: Use data from a randomized experiment to compare two treatments. Use simulations to decide if differences between parameters are significant.

AR.Math.Content.HSS.IC.B.6: Read and explain, in context, the validity of data from outside reports by: Identifying the variables as quantitative or categorical. Describing how the data was collected. Indicating any potential biases or flaws. Identifying inferences the author of the report made from sample data.

### AR.Math.Content.HSS.CP: Conditional Probability and the Rules of Probability

#### AR.Math.Content.HSS.CP.A: Understand independence and conditional probability and use them to interpret data

AR.Math.Content.HSS.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”).

AR.Math.Content.HSS.CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

AR.Math.Content.HSS.CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

AR.Math.Content.HSS.CP.A.4: 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. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

#### AR.Math.Content.HSS.CP.B: Use the rules of probability to compute probabilities of compound events.

AR.Math.Content.HSS.CP.B.6: Find the conditional probability of A given B.

AR.Math.Content.HSS.CP.B.8: 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.

AR.Math.Content.HSS.CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

AR.Math.Content.HSS.CP.B.10: Use visual representations in counting (e.g. combinations, permutations, etc.) including but not limited to: Venn diagrams, Tree diagrams.

### AR.Math.Content.HSS.MD: Using Probability to Make Decisions

#### AR.Math.Content.HSS.MD.A: Calculate expected values and use them to solve problems

AR.Math.Content.HSS.MD.A.2: Calculate the expected value of a random variable. Interpret the expected value of a random variable as the mean of the probability distribution.

AR.Math.Content.HSS.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.

AR.Math.Content.HSS.MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

#### AR.Math.Content.HSS.MD.B: Use probability to evaluate outcomes of decisions

AR.Math.Content.HSS.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. Evaluate and compare strategies on the basis of expected values.

AR.Math.Content.HSS.MD.B.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

AR.Math.Content.HSS.MD.B.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 9/16/2020

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