Students must compare measures of center and spread for two sets of data. This multiple-choice question is a sample item used in the 2005 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OAT item is also available in Microsoft® Word. The Ohio Department of Education Instructional Management System website allows visitors to search for test items by subject and grade band and build a printable database of questions using the Add to Your Backpack function. ODE Reference Information: 2005 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 41. (author/sw)

Students must analyze the effect on the mean and median of removing an outlier from a data set. This multiple-choice question is a sample item used in the 2008 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OAT item is also available in Microsoft® Word. The Ohio Department of Education Instructional Management System website allows visitors to search for test items by subject and grade band and build a printable database of questions using the Add to Your Backpack function. ODE Reference Information: 2008 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 25. (author/sw)

Students must interpret two box-and-whiskers plots to identify a true statement. This multiple-choice question is a sample item used in the 2007 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OAT item is also available in Microsoft® Word. The Ohio Department of Education Instructional Management System website allows visitors to search for test items by subject and grade band and build a printable database of questions using the Add to Your Backpack function. ODE Reference Information: 2007 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 34. (author/sw)

Students must interpret box-and-whiskers plots to find a difference of medians. This multiple-choice question is a sample item used in the 2005 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System). The URL link (above) takes the user directly to the test item (PDF), with access to performance data, complexity level of the item, and discussion of incorrect responses. This OAT item is also available in Microsoft® Word. The Ohio Department of Education Instructional Management System website allows visitors to search for test items by subject and grade band and build a printable database of questions using the Add to Your Backpack function. ODE Reference Information: 2005 Ohio Grade 8 Achievement Test for Mathematics, Annotated Item 34. (author/sw)

Students collect data on their study and TV viewing time over a period of several days. They use a graphing calculator, with step by step instructions, to find measures of central tendency, construct a box and whiskers graph, construct a scatter plot of class data, and look for a line of best fit. Activity sheets and suggestions for assessment are included. (author/sw)

Working in groups, students use a graphing calculator and the instructional activity sheets to gather data, calculate statistics, construct graphs, and make inferences. The students communicate their findings in a summary letter. The lesson is listed for grades 8-10 but reviewers felt the emphasis on measures of center made it better suited to grades 5-8. Activity sheets, interpretation questions, and extensions of the lesson are included. (author/sw)

Students investigate the average earnings of a movie in a given week using data they collect from web or print resources. In this investigation, students use the measures of center and different graphical displays of the data to make an argument that each of the measures of center may be appropriate, providing an explanation for their choice of mean, median, or mode. They identify outliers and create box plots (both modified and non-modified), histograms, and stem-and-leaf plots. Students also analyze spread and distribution of the data as part of their investigation. To conclude the exploration, students prepare a poster and give a report to the class. As students analyze actual data about a topic that engages them, they apply mathematics to a real-world situation and can see the value of the statistical concepts they are studying. Evaluation rubrics are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)

Q. Why is a box like a cat? A. Both have whiskers. Students collect data and learn how to represent the results using box-and-whiskers plots and stem-and-leaf plots. An extension of the problem and a complete discussion of the underlying statistical ideas are included. This mathematically rich problem was originally developed for the Project Discovery Mathematics by Inquiry institutes for middle grades teachers taught in 1992 - 1994 at Ohio State University. Project Discovery was co-funded by the Ohio Board of Regents and the Statewide Systemic Initiative (SSI) program of the National Science Foundation. (author/sw)