S.ID: Interpreting Categorical and Quantitative Data

S.ID.A: Summarize, represent, and interpret data on a single count or measurement variable. Use calculators, spreadsheets, and other technology as appropriate.

S.ID.A.2: Represent measurement data with plots on the real number line (dot plots, histograms, and box plots).

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

S.ID.A.3: Compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different variables, using statistics appropriate to the shape of the distribution for each measurement variable.

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

S.ID.A.4: Interpret differences in shape, center, and spread in the context of the variables accounting for possible effects of extreme data points (outliers) for measurement variables.

Describing Data Using Statistics
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions

S.ID.A.5: 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.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

S.ID.B: Summarize, represent, and interpret data on two categorical and quantitative variables.

S.ID.B.7: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.B.7.a: Fit a linear function to data where a scatter plot suggests a linear relationship and use the fitted function to solve problems in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

S.ID.B.7.c: Informally assess the fit of a function by plotting and analyzing residuals.

Least-Squares Best Fit Lines

S.ID.C: Interpret linear models.

S.ID.C.8: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

S.ID.C.9: Compute (using technology) and interpret the linear correlation coefficient.

Correlation

S.ID.C.10: Distinguish between (linear) correlation and causation.

Correlation

S.IC: Making Inferences and Justifying Conclusions

S.IC.A: Understand and evaluate random processes underlying statistical studies. Use calculators, spreadsheets, and other technology as appropriate.

S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Polling: City
Populations and Samples

S.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

S.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Estimating Population Size
Polling: City
Polling: Neighborhood
Populations and Samples

S.IC.B.4: Use data from a sample survey to estimate a population mean or proportion and a margin of error.

Polling: City
Populations and Samples

S.IC.B.6: Evaluate reports of statistical information based on data.

Polling: City

S.CP: Conditional Probability and the Rules of Probability

S.CP.A: Understand independence and conditional probability and use them to interpret data from simulations or experiments.

S.CP.A.2: Demonstrate understanding 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

S.CP.A.3: Understand the conditional probability of A given B as P(intersection of 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

S.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

S.CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

S.CP.B.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the mode.

Independent and Dependent Events

S.CP.B.8: Apply the general Multiplication Rule in a uniform probability model P(intersection of 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

S.CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Permutations and Combinations

S.MD: Using Probability to Make Decisions

S.MD.A: Calculate expected values and use them to solve problems.

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.

Lucky Duck (Expected Value)

S.MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution of the variable.

Lucky Duck (Expected Value)

S.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.

Lucky Duck (Expected Value)

S.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.

Lucky Duck (Expected Value)

S.MD.B: Use probability to evaluate outcomes of decisions.

S.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

S.MD.B.5.a: Find the expected payoff for a game of chance.

Lucky Duck (Expected Value)

S.MD.B.5.b: Evaluate and compare strategies on the basis of expected values.

Lucky Duck (Expected Value)