# Interpreting Statistics: A Case of Muddying the Waters

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## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students are able to: interpret data and evaluate statistical summaries; and critique someone elseŐs interpretations of data and evaluations of statistical summaries. The lesson also introduces students to the dangers of misapplying simple statistics in real-world contexts, and illustrates some of the common abuses of statistics and charts found in the media.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution Non-Commercial No Derivatives
- Media Format:
- Downloadable docs, Text/HTML

## Standards

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: Informally assess the fit of a function by plotting and analyzing residuals.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: Fit a linear function for a scatter plot that suggests a linear association.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Interpret linear models

Standard: Compute (using technology) and interpret the correlation coefficient of a linear fit.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Standard: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.*

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on two categorical and quantitative variables

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Standard: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Interpret linear models

Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsStandard: Evaluate reports based on data.*

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Interpret linear models

Standard: Distinguish between correlation and causation.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on a single count or measurement variable

Standard: Represent data with plots on the real number line (dot plots, histograms, and box plots).*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on a single count or measurement variable

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on a single count or measurement variable

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

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Interpreting Categorical and Quantitative DataCluster: Summarize, represent, and interpret data on a single count or measurement variable

Standard: 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.*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsCluster: Understand and evaluate random processes underlying statistical experiments

Standard: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Statistics and Probability: Making Inferences and Justifying ConclusionsCluster: Understand and evaluate random processes underlying statistical experiments

Standard: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Standard: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Indicator: Evaluate reports based on data.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Standard: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Indicator: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Standard: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Indicator: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: Fit a linear function for a scatter plot that suggests a linear association.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

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

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: Represent data with plots on the real number line (dot plots, histograms, and box plots).*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: Informally assess the fit of a function by plotting and analyzing residuals.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

Standard: Interpret linear models

Indicator: Distinguish between correlation and causation.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

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

Indicator: 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.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Standard: Understand and evaluate random processes underlying statistical experiments

Indicator: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

Standard: Interpret linear models

Indicator: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Making Inferences and Justifying Conclusions

Standard: Understand and evaluate random processes underlying statistical experiments

Indicator: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a row cause you to question the model?*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability: Interpreting Categorical and Quantitative Data

Standard: Interpret linear models

Indicator: Compute (using technology) and interpret the correlation coefficient of a linear fit.*

Degree of Alignment: Not Rated (0 users)

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# Tags (9)

- Mathematics
- CCSS
- Common Core Math
- Common Core PD
- Data Interpretation
- ODE Learning
- Real World Math
- Statistics and Probability
- assessment

## Comments