# Comparing Sets of Data Grade Eight

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2 Ohio Standards Connection: Related Benchmark A Create, interpret and use graphical displays and statistical measures to describe data; e.g. box-andwhisker plots, histograms, scatterplots, measures of center and variability. Indicator 1 Use, create, and interpret scatterplots and other types of graphs as appropriate. Mathematical Processes Benchmarks A. Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution. D. Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions. E. Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas. Facilitate a discussion of the various terms and statistical measures identified by students. Use a round- robin strategy by asking each pair of students for one term or measure from their list. Write responses on chart paper, the board or a transparency. Lead students in a discussion of the terms and measures on the list. Ask students to define the terms, tell how to find them and what they indicate about the data. Extend the discussion, as needed, to include a review of key prerequisite terms and measures for the lesson; e.g., mean, median, mode and range. Some terms that may or may not be identified initially include outlier, quartile and interquartile range, terms generally used to describe larger data sets than in the pre-assessment activity. Scoring Guidelines: Use the activity to identify students needs and, if needed, to determine the level of review or additional instruction required. Students responses are not scored. Post-Assessment: Students complete three tasks designed to assess knowledge and skills in comparing two sets of data using measures of center and spread, Attachment B, Post-Assessment Activity. Scoring Guidelines: Use Attachment C, Post-Assessment Answer Key to guide scoring. Instructional Procedures: Part One Instructional Tip: Complete this component the day before the lesson to more efficiently implement the lesson activities. 2

8 quartile range Comparing Sets of Data Grade Eight Technology Connections: Use calculators or graphing calculators to find the measures of center, spread, and box-andwhisker plots. Use presentation software to create data displays. Use data analysis or statistics program to compute measures of center and spread and to create box-and-whisker plots. Use computer-based survey tools to design survey, collect data on-line, and summarize survey responses. Research Connections: Zorfass, Judith, & Harriet Copel. The I-Search: Guiding Students Toward Relevant Research. Educational Leadership. 53 (1995) Arter, Judith and Jay McTighe. Scoring Rubrics in the Classroom: Using Performance Criteria for Assessing and Improving Student Performance. Thousand Oaks, Ca: Corwin Press, Attachments: Attachment A, Pre-Assessment Activity Attachment B, Post-Assessment Activity Attachment C, Post-Assessment Answer Key Attachment D, Survey Form Attachment E, Sample Survey Questions Attachment F, Shoe Size Data Collection Forms Attachment G, If the Shoe Fits Activity 8

9 Attachment A Pre-Assessment Activity Name Date Directions: Think about terms and statistical measures that can be used to describe the set of data listed below Use the table below to record terms and statistical measures that can be used to describe the data. List as many different terms and statistical measures as you can in the time permitted. Terms Statistical Measures 9

10 Attachment B Post-Assessment Activity Name Date Mr. Brown and Mrs. Smith each gave their class the same 20-point quiz. The scores for each class are listed below: Quiz Scores for Mr. Brown s Class: Quiz Scores Mrs. Smith s Class: Task 1: Find the mean, median, mode, range, quartiles and interquartile range for each class and write the values in the table below. Statistical Measure Mr. Brown s Class Mrs. Smith s Class Mean Median Mode Range First Quartile Third Quartile Interquartile Range 10

12 Attachment C Post-Assessment Answer Key Task 1: Statistical Measure Mr. Brown s Class Mrs. Smith s Class Mean Median Mode Range First Quartile Third Quartile Interquartile Range Task 2: Create a box-and-whisker plot for the data for each class. Attachment C (Continued) Post-Assessment Answer Key 12

14 Attachment D Survey Form Name Date 1. Question Response #1 Response #2 Response #

15 Attachment E Sample Survey Questions How many ounces of water do you drink in a day? How many hours do you sleep on an average night? What is your resting heart rate in beats per minute? How many minutes a day do you watch television? What size shoe do you wear? How many calories do you consume in a day? How many minutes a night do you spend doing homework/work? How many phone calls do you make on an average day? How far is your commute to school/work? How many times do you brush your teeth on a daily (or weekly) basis? How many siblings do you have? How much money do you spend on lunch each day? 15

16 Attachment F Shoe Size Data Collection Forms 16

17 Attachment G If the Shoe Fits Activity Name Date List the data for your class in increasing order. Shoe Sizes Reported by Students Shoe Sizes Reported by Students Task 1: Find the mean, median, mode, range, quartiles and interquartile range for each set of data and write the values in the table below. Statistical Measure Mean Shoe Sizes Reported by Students Shoe Sizes Reported by Students Median Mode Range First Quartile Third Quartile Interquartile Range 17

18 Attachment G (Continued) If the Shoe Fits Activity Task 2: Create a box-and-whisker plot for each set of data. Task 3: Describe how the shoe size data sets are similar and how they are different. Use mathematical terms and statistical measures to explain and support your answers. 18

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