Mathematics » High School: Statistics & Probability » Interpreting Categorical & Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable

• 1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

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• 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.

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• 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

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• 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.

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Summarize, represent, and interpret data on two categorical and quantitative variables

• 5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

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• 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

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  • a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

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  • b. Informally assess the fit of a function by plotting and analyzing residuals.

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  • c. Fit a linear function for a scatter plot that suggests a linear association.

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Interpret linear models

• 7. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

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• 8. Compute (using technology) and interpret the correlation coefficient of a linear fit.

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• 9. Distinguish between correlation and causation.

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