Math Focal Points
Table Of Contents
Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets.
Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center. Students select the mean or the median as the appropriate measure of center for a given purpose (NCTM, 2006, p.20).
As reflected in this set of resources, the emphasis here is on understanding descriptive statistics; in particular, measures of center. You will find tutorials, lesson ideas, problems, and applets for teaching these topics, and even full projects that can involve your middle school students in worldwide data collection.
Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how these statistics change (or, in some cases, how they don't change).
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Written for the student, this tutorial on mean, median, and mode includes fact sheets on the most basic concepts, plus practice sheets and a quiz. Key ideas are clearly defined at the student level through graphics as well as text.
(From Numbers : Handling data — MSP full record)
Users click to easily and quickly build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. An efficient tool for viewing these statistics visually.
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This activity challenges students to interpret a bar graph, showing only percentages, to determine the mean number of hours teenagers work per week. A more complicated and interesting problem than it may seem at first glance! A hint suggests that students assume that 100 students participated in the survey; a full solution sets out the math in detail. Related questions ask students to calculate averages for additional data sets.
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Can your students find the mean, median, and mode from a stem-and-leaf plot? They can use this applet to explore the measures of center in relation to the stem-and-leaf presentation of data. Students use the online plotter to enter as much data as they choose; then they determine measures of center and have the program check and correct their values. Ideas for class practice and discussion are provided in a lesson outline.
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In this interactive game, students compute the mean, median, and range of the running times of four trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.
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This interactive tool allows students to compare measures of central tendency. As students change one or more of the seven data points, the effects on the mean and median are immediately displayed. Questions challenge students to explore further the use of these measures of center; for example, What happens if you pull some of the data values way off to one extreme or the other extreme?
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This web site allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students can participate in the project each spring, April-June. Students learn to collect, organize, and interpret data. You will find project information, lesson plans, and implementation assistance at the site.
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This Internet-based collaborative project will allow students to share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students will determine the average amount of water used by one person in a day. Students must develop a hypothesis, conduct an experiment, and present their results.
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Resources that firmly place data analysis in context! The lessons and interdisciplinary projects were selected to promote student interest by focusing on real-world situations and developing skills for using the power of mathematics to form important conclusions relevant to life. Students learn that working with data offers insights into society’s problems and issues.
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Reference
NCTM. (2006).
Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author
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Copyright
May 2008 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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