Algebra 1
Unit 4: Descriptive Statistics
Students will choose and create an appropriate data representation for a given set of data. They will be able to read and interpret the representations they create as well as others that are given to them. These data representations will include bar graphs, histograms, boxandwhisker plots, stem and leaf plots (including backtoback stem plots) as well as frequency tables. For categorical data, students will be able to use twoway frequency tables to find joint, marginal and conditional relative frequencies.
Students will calculate and use summary statistics such as mean, median, range, lower and upper quartile, interquartile range and standard deviation to help describe the shape of the data. The processes by which mean and median are calculated have been previously taught. Students have not been introduced to standard deviation, and must understand the process behind the calculation. However, technology should be used to calculate the standard deviation. Students will build on their understanding of these calculations to comment on possible outliers in a data set and to make wellinformed decisions about the best summary statistics to represent given data. When data is notably skewed or when meaningful outliers are present, the median and 5Number Summary should be used to describe the distribution. Alternately, the mean and standard deviation should be used to describe unimodal and symmetric data. Throughout this unit, students should use these summary statistics and/or graphical representations to write critical analyses of a situation within the context of the given data.
Students will calculate and use summary statistics such as mean, median, range, lower and upper quartile, interquartile range and standard deviation to help describe the shape of the data. The processes by which mean and median are calculated have been previously taught. Students have not been introduced to standard deviation, and must understand the process behind the calculation. However, technology should be used to calculate the standard deviation. Students will build on their understanding of these calculations to comment on possible outliers in a data set and to make wellinformed decisions about the best summary statistics to represent given data. When data is notably skewed or when meaningful outliers are present, the median and 5Number Summary should be used to describe the distribution. Alternately, the mean and standard deviation should be used to describe unimodal and symmetric data. Throughout this unit, students should use these summary statistics and/or graphical representations to write critical analyses of a situation within the context of the given data.
NOTE  The "Background Info. and Guided Practice" links require a free registration to use the LearnZillion content. Parents can create a free "Teacher" account here. Once logged in you can access the "Background Info. & Guided Practice" videos without interruption.
What will my child learn?
Students will:
Summarize, represent, and interpret data on a single count or measurement variable.
S.ID.A.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
S.ID.A.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 sets.
S.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers) (SAT® Content  PSDA.09).
Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.B.5
Summarize categorical data for two categories in twoway 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 (SAT® Content  PSDA.07). (Note: Students currently in high school have been introduced to twoway tables last year. Students currently in Grades 7 & 8 have not been introduced to twoway tables.)
Students will:
Summarize, represent, and interpret data on a single count or measurement variable.
S.ID.A.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
 Background Info.
 Check for Understanding: Interpreting and Comparing Data Distributions
 Enrichment Tasks: Haircut Costs  1, 2, 3 Speed Trap
S.ID.A.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 sets.
 Background Info.
 Check for Understanding: Interpreting and Comparing Data Distributions  Standard Deviation of a Population
 Enrichment Tasks: Understanding Standard Deviation  Measuring Variability in a Data Set
S.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers) (SAT® Content  PSDA.09).
 Background Info.
 Check for Understanding: Exploring Standard Deviation  Interpreting and Comparing Data Distributions
 Enrichment Tasks: Describing Data Sets with Outliers  Identifying Outliers
Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.B.5
Summarize categorical data for two categories in twoway 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 (SAT® Content  PSDA.07). (Note: Students currently in high school have been introduced to twoway tables last year. Students currently in Grades 7 & 8 have not been introduced to twoway tables.)
 Check for Understanding: Trends in Categorical Data
 Enrichment Tasks: Musical Preferences
What are some signs of student mastery?

Tools and Technology
NCTM's Advanced Data Grapher can be used to build and analyze data using box plots, scatterplots, histograms, stemandleaf plots, and bubble graphs. You can enter multiple rows and columns of data, select which set(s) to display in a graph, and choose the type of representation. 'What's a dot plot?' See if this resource and accompanying video help deepen your understanding. 
More 4 U
How can students compare and analyze data distributions using a box plot? View an excerpt from a lesson that examines the statistics of four Major League baseball players. 