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).

Box-and-Whisker Plots
Histograms
Mean, Median, and Mode

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.

Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions

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).

Mean, Median, and Mode
Reaction Time 2 (Graphs and Statistics)

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.

Polling: City
Populations and Samples
Real-Time Histogram

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.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

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.

Cat and Mouse (Modeling with Linear Systems)

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

Correlation

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.

Polling: City
Polling: Neighborhood
Populations and Samples

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).

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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.

Polling: City
Polling: Neighborhood

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.

Polling: City
Polling: Neighborhood

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.

Polling: City
Polling: Neighborhood

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.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples
Real-Time Histogram

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”).

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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.

Independent and Dependent Events

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.

Independent and Dependent Events

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.

Histograms

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.

Independent and Dependent Events

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.

Independent and Dependent Events

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

Binomial Probabilities
Permutations and Combinations

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.

Binomial Probabilities
Permutations and Combinations

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.

Polling: City

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.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

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.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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.

Lucky Duck (Expected Value)

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

Lucky Duck (Expected Value)

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).

Lucky Duck (Expected Value)