PS.DA: Data Analysis

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
Graphing Skills
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)
Reaction Time 2 (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.

Populations and Samples

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
Populations and Samples
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.

Histograms

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.8: Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable.

Correlation
Histograms
Least-Squares Best Fit Lines
Lucky Duck (Expected Value)
Solving Using Trend Lines
Trends in Scatter Plots

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.

Polling: City
Polling: Neighborhood
Populations and Samples

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: Experimental Design

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

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
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.

Polling: City
Polling: Neighborhood

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.6: Model and solve real-world problems involving patterns using recursion and iteration, growth and decay, and compound interest.

Arithmetic Sequences
Compound Interest
Exponential Growth and Decay
Geometric Sequences
Half-life

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.

Correlation
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.

Polling: City
Polling: Neighborhood
Populations and Samples

PS.P: Probability

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

Binomial Probabilities

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
Geometric Probability
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
Geometric Probability
Independent and Dependent Events
Lucky Duck (Expected Value)
Permutations and Combinations
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

PS.P.4: Calculate the probabilities of complementary events.

Geometric Probability
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.

Lucky Duck (Expected Value)
Polling: City

PS.P.6: Analyze decisions and strategies using probability concepts. Analyze probabilities to interpret odds and risk of events.

Independent and Dependent Events
Lucky Duck (Expected Value)

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.

Lucky Duck (Expected Value)
Polling: City

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