Academic Standards

PS.DA.1: Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative frequency distribution functions, pie charts, scatterplots, stem-and-leaf plots, and box-and-whisker plots. Draw these with and without technology.

Box-and-Whisker Plots

Correlation

Histograms

Least-Squares Best Fit Lines

Polling: City

Populations and Samples

Real-Time Histogram

Sight vs. Sound Reactions

Solving Using Trend Lines

Stem-and-Leaf Plots

Trends in Scatter Plots

PS.DA.2: Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation. Use tables and technology to estimate areas under the normal curve. Fit a data set to a normal distribution and estimate population percentages. Recognize that there are data sets not normally distributed for which such procedures are inappropriate.

Box-and-Whisker Plots

Describing Data Using Statistics

Geometric Sequences

Mean, Median, and Mode

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Sight vs. Sound Reactions

Stem-and-Leaf Plots

PS.DA.3: Understand the central limit theorem and use it to solve problems.

PS.DA.4: Understand hypothesis tests of means and differences between means and use them to reach conclusions. Compute and use confidence intervals to make estimates. Construct and interpret margin of error and confidence intervals for population proportions.

Describing Data Using Statistics

Mean, Median, and Mode

Polling: City

Stem-and-Leaf Plots

PS.DA.6: 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.

PS.DA.7: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Polling: City

Polling: Neighborhood

Populations and Samples

PS.DA.9: Understand statistics and use sampling distributions as a process for making inferences about population parameters based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

PS.DA.10: 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.

PS.DA.11: Find linear models by using median fit and least squares regression methods to make predictions. Decide which among several linear models gives a better fit. Interpret the slope and intercept in terms of the original context. 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

PS.DA.12: Evaluate reports based on data by considering the source of the data, the design of the study, the way the data are analyzed and displayed, and whether the report confuses correlation with causation. Distinguish between correlation and causation.

Correlation

Polling: City

Polling: Neighborhood

Populations and Samples

PS.ED.1: Formulate questions that can be addressed with data. Collect, organize, and display relevant data to answer the questions formulated.

Correlation

Describing Data Using Statistics

Real-Time Histogram

Stem-and-Leaf Plots

PS.ED.3: Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

PS.ED.4: Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions.

Polling: City

Populations and Samples

PS.ED.5: Model and solve real-world problems using the geometric distribution or waiting-time distribution, with or without technology.

Box-and-Whisker Plots

Describing Data Using Statistics

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

PS.ED.7: Understand and apply basic ideas related to the design, analysis, and interpretation of surveys and sampling, such as background information, random sampling, causality and bias.

Polling: City

Polling: Neighborhood

Populations and Samples

PS.ED.9: Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.

PS.P.1: Understand and use the addition rule to calculate probabilities for mutually exclusive and nonmutually exclusive events.

PS.P.2: Understand and use the multiplication rule to calculate probabilities for independent and dependent events. 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.

Binomial Probabilities

Independent and Dependent Events

PS.P.3: Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.

Binomial Probabilities

Permutations and Combinations

Probability Simulations

Theoretical and Experimental Probability

PS.P.5: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

PS.P.7: 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.

PS.P.8: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; Compute and interpret the expected value of random variables.

Binomial Probabilities

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

PS.P.9: Derive the binomial theorem by combinatorics. Use combinatorial reasoning to solve problems.

Binomial Probabilities

Permutations and Combinations

PS.P.10: 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.

Independent and Dependent Events

Correlation last revised: 1/22/2020