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Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

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Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

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Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

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Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

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Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

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Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

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Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

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Investigate patterns of association in bivariate data.

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Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

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Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

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Draw informal comparative inferences about two populations.

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Use random sampling to draw inferences about a population.

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Summarize and describe distributions.

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Summarize numerical data sets in relation to their context, such as by:  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

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Summarize numerical data sets in relation to their context, such as by:  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

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Summarize numerical data sets in relation to their context, such as by:  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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Summarize numerical data sets in relation to their context, such as by:  Reporting the number of observations.

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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

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Develop understanding of statistical variability.

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Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

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Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.