Algebra 1 (& GT)
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.
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).
 Check for Understanding: Comparing Data Distributions
 Review/Rewind: Comparing Means and Medians
 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.
 Check for Understanding: Comparing Data Distributions  Standard Deviation of a Population
 Review/Rewind: Measures of Spread
 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).
 Check for Understanding: Comparing Data Distributions
 Review/Rewind: Population Standard Deviation
 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
 Review/Rewind: Categorical Data (in TwoWay Tables)
 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. Measure of Central Tendency  This online game from PBS allow students to earn points by answering questions on the measure of central tendency. This online game gives a glossary and continuous explanations on the measures of central tendency. This game is free and does not require a download. Two Way Tables  This free online program will help students design, use and interpret two way tables for recording and sorting discrete data This program does not require a download and has an easy, medium, and hard setting. 
More 4 U
'What's a dot plot?' See if this resource and accompanying video help deepen your understanding. 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. 
Go on to 5. Volumes of Solid Figures