CCSS.Math.Content.HSS-ID: Interpreting Categorical and Quantitative Data

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

CCSS.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
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

CCSS.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
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

CCSS.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).

Populations and Samples
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

CCSS.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, spreadsheets, and tables to estimate areas under the normal curve.

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

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

CCSS.Math.Content.HSS-ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

CCSS.Math.Content.HSS-ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

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

CCSS.Math.Content.HSS-ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.

Least-Squares Best Fit Lines

CCSS.Math.Content.HSS-ID.B.6.c: Fit a linear function for a scatter plot that suggests a linear association.

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

CCSS.Math.Content.HSS-ID.C: Interpret linear models

CCSS.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.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

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

Correlation

CCSS.Math.Content.HSS-ID.C.9: Distinguish between correlation and causation.

Correlation

CCSS.Math.Content.HSS-IC: Making Inferences and Justifying Conclusions

CCSS.Math.Content.HSS-IC.A: Understand and evaluate random processes underlying statistical experiments

CCSS.Math.Content.HSS-IC.A.1: Understand 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

CCSS.Math.Content.HSS-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Geometric Probability
Probability Simulations
Theoretical and Experimental Probability

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

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

Polling: City
Polling: Neighborhood

CCSS.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

CCSS.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.

Populations and Samples

CCSS.Math.Content.HSS-CP: Conditional Probability and the Rules of Probability

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

CCSS.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

CCSS.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

CCSS.Math.Content.HSS-CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

CCSS.Math.Content.HSS-CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model

CCSS.Math.Content.HSS-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 model.

Independent and Dependent Events

CCSS.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

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

Permutations and Combinations

CCSS.Math.Content.HSS-MD: Using Probability to Make Decisions

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

CCSS.Math.Content.HSS-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)

CCSS.Math.Content.HSS-MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Lucky Duck (Expected Value)

CCSS.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.

Lucky Duck (Expected Value)

CCSS.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.

Lucky Duck (Expected Value)

CCSS.Math.Content.HSS-MD.B: Use probability to evaluate outcomes of decisions

CCSS.Math.Content.HSS-MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

CCSS.Math.Content.HSS-MD.B.5.a: Find the expected payoff for a game of chance.

Lucky Duck (Expected Value)

CCSS.Math.Content.HSS-MD.B.5.b: Evaluate and compare strategies on the basis of expected values.

Lucky Duck (Expected Value)

CCSS.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)

CCSS.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)