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1 Ohio Standards Connection Data Analysis and Probability Benchmark F Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data. Indicator 3 Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. Mathematical Processes Benchmarks J. Communicate mathematical thinking to others and analyze the mathematical thinking of others. K. Recognize and use mathematical language and symbols when reading, writing and conversing with others. Lesson Summary: In this lesson, students learn about statistical measures using the heights of the students in the class. They measure and order the heights to find the range, first quartile and third quartile. They learn to calculate the interquartile range by finding the difference of the first quartile and third quartile. Students practice determining the statistics of sets of data and compare the statistics. Estimated Duration: One and one-half to two hours Commentary: Students have some conception of measures of spread and exploring range from experiences with data in the elementary grades. Students have experience in describing, organizing, representing and analyzing data. This experience progresses over the years from informal descriptions in earlier grades to using technology to analyze and represent in the middle grades. Students begin to use statistical terms in the analysis of the data sets. Pre-Assessment: Students create concept maps to demonstrate their knowledge and understanding of the concepts related to measures of center (mean, median and mode), measures of spread (range, quartiles, interquartile range, extremes) and outliers. The pre-assessment also assesses students knowledge of ways to display data (boxand-whisker plot, stem-and-leaf plot and frequency tables). The second part of this pre-assessment requires students to discuss their ideas in small groups and develop a group concept map that will scaffold their thinking in preparation for the lesson. Have each student cut out the vocabulary cards from Measures of Spread, Attachment A. Instruct students to create a concept map by grouping cards in ways that seem to go together best and make the most sense. A sample organizer is included on Attachment B. Instructional Tip: A concept map is a special form of diagram for showing connections among concepts. Concept mapping can be used for several purposes: to generate ideas, communicate complex ideas, aid learning by explicitly integrating new and old knowledge and assess understanding or diagnose misunderstanding. Have students glue the cards on paper and give each group a title that best describes its characteristics. As an option, have students complete the activity on paper. 1

6 Attachment A Measures of Spread: Pre-Assessment Name Date Directions: Cut out the cards below. Arrange them into groups based on a commonality. Name each group. Describe why you grouped the words the way you did. Record your ideas on paper. Box-and-whisker plot Interquartile range Lower quartile Mean Measures of center Measures of spread Median Mode Range Upper quartile Stem-and-leaf plot Frequency table Lower extreme Upper extreme 6

8 Attachment C Olympia Diving Team Problem Name Date Directions: Analyze each diver s performance using the data given. Larry and Leslie are on the Olympia Middle School diving team. In a recent competition, they were awarded points by three judges on twelve separate dives. Their total scores for each dive are as follows: Dive Larry s Leslie s Score Score Mean Median Range Lower Quartile Upper Quartile Interquartile Range 1. Calculate the mean, median, range, upper and lower quartiles, and interquartile range for each of their sets of scores. 2. Write a description about the diving performances of Larry and Leslie based on the data above.

9 Attachment C (continued) Olympia Diving Team Problem Name Date 3. a. Who is the more consistent diver? b. Why? c. How could you show that Leslie is more consistent? 4. Organize your data into a graphical display (box-and-whisker plot, stem-and-leaf plot, frequency table, etc.) that compares the performances of the two divers.

10 Attachment D Olympia Diving Team Problem Answer Key Dive Larry s Leslie s Score Score Mean 22 ~23.4 Median Range Lower Quartile Upper Quartile Interquartile Range A sample response: Leslie s performance is better but less consistent. Leslie s mean is slightly higher and her median (middle) is 3.5 points higher than Larry s. Twenty-five percent of her dives scored at or above 27 while Larry s highest 25 percent were only at or above However, Leslie s scores have a wider overall range, making her less consistent. 3. Sample response: Larry is more consistent because the range of his scores is 16 while Leslie s range is 22. c. If the lower scores for each are removed, Leslie is more consistent. 4.

11 Attachment E Measures of Spread Post-Assessment Name Date Directions: Answer each of the questions based on the data given. You may use a calculator if needed. Ages of people at the movies last Saturday afternoon Organize the data into a graphical display (box-and-whisker plot, stem-and-leaf plot, frequency table, etc.) that best reflects the data. Attach to a separate sheet. 2. What is the range of the data? Show how you found it. 3. Find the lower quartile, upper quartile, median and Interquartile range. Lower quartile: Median: Upper quartile: Interquartile range: 4. Write a description about the attendance at the movie for last Saturday afternoon.

12 Attachment F Measures of Spread Post-Assessment Answer Key Ages of people at the movies last Saturday afternoon Organize the data into a graphical display of some kind (box-and-whisker plot, stem-and-leaf plot, frequency table, etc.) that best reflects the data. Explain why box-and-whisker plot is best here or ask students to do box-and-whisker plot only What is the range of the data? Show how you found it = Find the lower quartile, upper quartile, median and Interquartile range. Lower quartile: 11 Upper quartile: 15.5 Median: 14 Interquartile range: Are there any outlier(s). If so, what are they? Yes; 47 is an outlier 5. Answers will vary. Ideas may include: the 47-year-old person is the owner of the movie theater; the older teenagers probably work there; the movie is probably a movie that middle school students would like.

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