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
 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.

 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
 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.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

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.

 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.

 Polling: City

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.

 Polling: Neighborhood

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
 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.

 Polling: City

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.

 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
 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: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.