Interpreting Categorical and Quantitative Data (ID)
Summarize, represent, and interpret data on a single count or measurement variable
Represent data with plots on the real number line (dot plots, histograms, and box plots).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Represent (data)
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2 - I can represent data with dot plots, histograms or box plots on a real number line.
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A. A variety of plot types can be used to represent data on a real number line.
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A.1 What are the types of data plots on real number line?
A.2 How are the various types of data plots on the real number line alike or different?
A.3 What factors affect the choice of plot type for a data set?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Statistics
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3 - Use (statistics appropriate to the shape of a data distribution)
4 - Compare (center, median, mean of two or more data sets)
4 - Compare (spread, interquartile range, standard deviation of two or more data sets)
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3 - I can use the statistic appropriate to the shape of a data distribution to compare central tendencies of median and mean of two or more different data sets.
3 - I can use the statistic appropriate to the shape of a data distribution to compare
1 - I can use data spread of interquartile range and standard deviation of two or more different data sets to compare.
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A. The shape of a data distribution plays a key role in the choice of the appropriate statistic used to compare central tendencies and spread of two or more different data sets.
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A.1 How does the shape of a data distribution affect the choice of the appropriate statistic in comparison of central tendencies of different data sets?
A.2 How does the shape of a data distribution affect the choice of the appropriate statistic in comparison of spread in different data sets?
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Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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3 - Interpret (differences in shape, center, and spread in context of data sets)
4 - Account for (possible effects of extreme data points or outliers.)
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3 - I can interpret differences in shape, center, and spread in the context of data sets.
4 - I can account for possible effects on the shape, center and spread of data produced by extreme data points or outliers.
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A. The context of data sets can reveal information about differences in shape, center, and spread of the data.
B. Outliers or extreme data points can produce various effects on the shape, center and spread of a data set.
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A.1 How can the context of a data set reveal information about differences in the shape, center, and spread of the data?
B.1 What effects can outliers produce on the shape, center, and spread of a data set?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Data Set
Normal Distribution
Normal Curve
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3 - Use (mean, standard deviation)
3 - Fit (data set to normal distribution)
3 - Estimate (population percentages)
2 - Recognize (data sets that cannot be fit to a normal distribution)
3 - Use (calculators, spreadsheets and tables)
3 - Estimate (areas under the normal curve by using calculators, spreadsheets, and tables)
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3 - I can use mean and standard deviation.
3 - I can fit a data set to a normal distribution by use of mean and standard deviation.
3 - I can estimate population percentages by use of mean, standard deviation, and normal distribution.
2 - I can recognize that some data sets cannot be fit to a normal distribution.
3 - I can use calculators, spreadsheets, and tables to find areas.
3 - I can estimate areas under the normal curve by using calculators, spreadsheets, and tables.
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A. The mean and standard deviation of a data set can be used to fit the data to a normal distribution.
B. The mean, standard deviation, and normal distribution can be used to estimate population percentages.
C. Some data sets cannot be fit to a normal curve.
D. Calculators, spreadsheets, and tables are methods to estimate areas under the normal curve.
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A.1 What is a normal distribution?
A.2 How can the mean and standard deviation of a data set be used to fit it to a normal distribution?
B.1 How can mean, standard deviation, and normal distribution be used to estimate population percentages?
C.1 Why are some data sets not appropriate to fit to a normal distribution?
D.1 How can calculators, spreadsheets, and tables be used to estimate areas under the normal curve?
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Summarize, represent, and interpret data on two categorical and quantitative variables
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Data
Categories
Tables
Frequencies
Associations
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2 - Summarize (categorical data for two categories in two-way frequency tables)
3 - Interpret (relative frequencies in context, to include joint, marginal, and conditional relative frequencies)
2 - Recognize (associations)
2 - Recognize (trends)
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2 - I can summarize categorical data for two categories in a two-way frequency table.
3 - I can interpret relative frequencies, including joint, marginal, and conditional relative frequencies, within the context of the data.
2 - I can recognize associations.
2 - I can recognize trends.
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A. Categorical data for two categories can be summarized in a two-way frequency table.
B. Relative frequencies, including joint, marginal, and conditional relative frequencies can be interpreted within the context of the data.
C. Two way-frequency tables promote the recognition of possible associations and trends in categorical data.
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A.1 What is categorical data?
A.2 What is a two-way frequency table?
A.3 How can categorical data for two categories be summarized in a two-way frequency table?
B.1 What is a relative frequency?
B.2 How are joint, marginal and conditional relative frequencies alike and/or different?
B.3 How can relative frequencies, joint, marginal, and conditional relative frequencies be interpreted within the context of a categorical data set?
C.1 How does a two-way frequency table promote the recognition of possible associations and trends in data?
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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Represent (data on 2 quantitative variables on scatterplot)
2 - Describe (relationship between variables)
3 - Fit (function to data [a])
2 - Solve (problems in context of data with function [a])
3 - Assess (fit of function [b])
3 - Plot (residuals [b])
3 - Analyze (residuals [b])
3 - Fit (linear function to scatterplot that suggests linear association [c])
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2 - I can represent data on 2 quantitative variables on scatterplot.
2 - I can describe relationship between variables.
3 - I can fit function to data [a].
2 - I can solve problems in context of data with function [a].
3 - I can assess fit of function [b].
3 - I can plot residuals [b].
3 - I can analyze residuals [b].
3 - I can fit linear function to scatterplot that suggests linear association [c].
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A. One can graph a data set and find a function that fits that data from the graph.
B. One can solve problems from the function based on the data graph.
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A.1 How can I look at data and figure out what function it might represent?
B.1 How can I use a set of data to solve a problem?
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Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Model
Slope
Intercept
Data
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3 - Interpret (slope as rate of change in context of data)
3 - Interpret (intercept (constant term)
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3 - I can interpret slope (rate of change) of a linear model in context of data.
3 - I can interpret the intercept (constant term) of a linear model in context of data.
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A. The slope of a linear model can be interpreted as a rate of change in the context of a data set.
B. The intercept of a linear model can be interpreted as the constant term in the context of a data set.
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A.1 In context of given data, how can slope be interpreted as rate of change in a linear model?
B.1 In context of given data, how can the intercept be interpreted as the constant term in a linear model?
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Compute (using technology) and interpret the correlation coefficient of a linear fit.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Correlation Coefficient
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3 - Compute (correlation coefficient)
3 - Use (technology)
3 - Interpret (correlation coefficient)
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3 - I can use technology to perform a computation.
3 - I can compute the correlation coefficient of a linear fit using technology.
3 - I can interpret the correlation coefficient of a linear fit.
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A. For a set of data technology can be used to compute the correlation coefficient of a linear fit.
B. The value of the correlation coefficient can be interpreted in various ways as a measure of how nearly the data falls on a straight line.
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A.1 What is a correlation coefficient of a linear fit?
A.2 How is a correlation coefficient computed using technology?
B.1 What information does the value of the correlation coefficient of a linear fit reveal about the data?
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Distinguish between correlation and causation.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Relationships
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4 - Distinguish (between correlation and causation)
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4 - I can distinguish between correlation and causation.
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A. Correlation and causation describe different aspects of the relationship between two variables.
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A.1 What is the meaning of correlation?
A.2 What is the meaning of causation?
A.3 How are correlation and causation related?
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