Choose a summary statistic appropriate to thecharacteristics of the data distribution,such as the shape of the distribution or the existence of extreme data points
Use regression techniques to describe approximately linear relationships betweenquantities.
Use graphical representations and knowledge of the context to make judgments aboutthe appropriateness of linear models
Look at residuals to analyze the goodness of fit.
Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables.
ENDURING UNDERSTANDINGS
Data are gathered, displayed, summarized, examined, and interpreted to discover patterns and deviations from patterns.
Which statistics to compare, which plots to use, and what the results of a comparison might mean, depend on the question to be investigated and the real-life actions to be taken.
Understand and be able to use the context of the data to explain why its distribution takes on a particular shape (e.g. are there real-life limits to the values of the data that force skewness?)
When making statistical models, technology is valuable for varying assumptions, exploring consequences and comparing predictions with data.
Causation implies correlation yet correlation does not imply causation
KEY STANDARDS
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable.
MCC9-12.S.ID.1Represent data with plots on the real number line (dot plots,histograms,and box plots).Choose appropriate graphs to be consistent with numerical data: dot plots,histograms, and box plots.MCC9-12.S.ID.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread(interquartile range, Mean Absolute Deviation) of two or more different data sets.MCC9-12.S.ID.3Interpret differences in shape, center, and spread in the context of thedata sets, accounting for possible effects of extreme data points (outliers). Students will examine graphical representations to determine if data are symmetric, skewed left, or skewed right and how the shape of the data affects descriptive statistics.
Summarize, represent, and interpret data on two categorical and quantitative variables.
MCC9-12.S.ID.5Summarize categorical data for two categories in two-way frequencytables. Interpret relative frequencies in the context of the data (including joint, marginal,and conditional relative frequencies). Recognize possible associations and trends in the data.MCC9-12.S.ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MCC9-12.S.ID.6aFit 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 thecontext. Emphasize linear, quadratic,and exponential models.MCC9-12.S.ID.6bInformally assess the fit of a function by plotting and analyzing residuals.MCC9-12.S.ID.6cFit a linear function for a scatter plot that suggests a linear association.
Interpret linear models
MCC9-12.S.ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.MCC9-12.S.ID.8Compute (using technology) and interpret the correlation coefficient of alinear fit.MCC9-12.S.ID.9Distinguish between correlation and causation
Walch Materials
Lesson 1: Working with a single measurement variable
CA Unit 4: Describing Data
Review Notes and Problems from Cherokee County
Ga DOE Frameworks - Student Edition
Calculating Correlation coefficient
http://www.statisticshowto.com/articles/how-to-compute-pearsons-correlation-coefficients/
Objectives:
In this unit student will:ENDURING UNDERSTANDINGS
KEY STANDARDS
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable.
MCC9-12.S.ID.1Represent data with plots on the real number line (dot plots,histograms,and box plots).Choose appropriate graphs to be consistent with numerical data: dot plots,histograms, and box plots.MCC9-12.S.ID.2Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread(interquartile range, Mean Absolute Deviation) of two or more different data sets.MCC9-12.S.ID.3Interpret differences in shape, center, and spread in the context of thedata sets, accounting for possible effects of extreme data points (outliers). Students will examine graphical representations to determine if data are symmetric, skewed left, or skewed right and how the shape of the data affects descriptive statistics.Summarize, represent, and interpret data on two categorical and quantitative variables.
MCC9-12.S.ID.5Summarize categorical data for two categories in two-way frequencytables. Interpret relative frequencies in the context of the data (including joint, marginal,and conditional relative frequencies). Recognize possible associations and trends in the data.MCC9-12.S.ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MCC9-12.S.ID.6aFit 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 thecontext. Emphasize linear, quadratic,and exponential models.MCC9-12.S.ID.6bInformally assess the fit of a function by plotting and analyzing residuals.MCC9-12.S.ID.6cFit a linear function for a scatter plot that suggests a linear association.Interpret linear models
MCC9-12.S.ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.MCC9-12.S.ID.8Compute (using technology) and interpret the correlation coefficient of alinear fit.MCC9-12.S.ID.9Distinguish between correlation and causationWalch Materials
Lesson 1: Working with a single measurement variable
Lesson 2: Working with two categorical and quantitative variables
Lesson 3: Interpreting linear models