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Lesson 12-2 Measures of Variation Contents

Example 2 Interquartile Range Example 3 Interpret and Compare Data Example 1 Range Example 2 Interquartile Range Example 3 Interpret and Compare Data Lesson 2 Contents

{$79, $42, $38, $51, $63, $91} Find the range of the set of data. The greatest value is $91, and the least value is $38. Answer: The range is $91 – $38 or $53. Example 2-1a

Find the range of the set of data. Stem 3 4 5 Leaf 3 3 5 7 7 8 0 3 3 4 9 4 9 The greatest value is 59, and the least value is 33. Answer: The range is 59 – 33 or 26. Example 2-1b

Find the range of each set of data. a. {14, 37, 82, 45, 24, 10, 75} b. Stem 5 6 7 Leaf 2 3 5 5 9 4 8 9 0 1 8 9 Answer: 72 Answer: 27 Example 2-1c

Find the interquartile range for the set of data. {38, 40, 32, 34, 36, 45, 33} Step 1 List the data from least to greatest. Then find the median. 32 33 34 36 38 40 45 Step 2 Find the upper and lower quartiles. LQ lower half UQ upper half median Example 2-2a

Answer: The interquartile range is 40 – 33 or 7. Example 2-2b

Find the interquartile range for the set of data. {2, 27, 17, 14, 14, 22, 15, 32, 24, 25} Step 1 List the data from least to greatest. Then find the median. 2 14 14 15 17 22 24 25 27 32 Step 2 Find the upper and lower quartiles. LQ lower half UQ upper half Example 2-2c

Answer: The interquartile range is 25 – 14 or 11. Example 2-2d

Find the interquartile range for each set of data. a. {52, 74, 98, 80, 63, 84, 77} b. {12, 18, 25, 31, 23, 19, 16, 22, 28, 32} Answer: 21 Answer: 10 Example 2-2e

Western States Eastern States 1 1 1 1 1 0 0 0 Land Use The urban land in certain western and eastern states is listed below as the percent of each state’s total land, rounded to the nearest percent. Western States Eastern States 1 1 1 1 1 0 0 0 3 2 2 2 1 1 1 0 3 3 4 5 6 6 8 5 4 4 0 8 9 9 9 9 9 9 1 1 3 3 4 4 5 2 3 6 7 3 5 Source: U.S. Census Bureau Example 2-3a

What is the median percent of urban land use for each region? Answer: The median percent of urban land use for the western states is 1%. The median percent of urban land use for the eastern states is 9% Example 2-3b

Compare the range for each set of data. Answer: The range for the west is 5% – 0% or 5%, and the range for the east is 35% – 3% or 32%. The percents of urban land in the east use vary more. Example 2-3c

Exercise The hours per week spent exercising for teenagers and people in their twenties are listed in the stem-and-leaf plot. Teens Twenties 5 4 2 0 0 0 4 6 7 9 7 3 1 0 2 2 5 1 2 0 3 4 5 8 Example 2-3d

a. What is the median time spent exercising for each group? b. Compare the range for each set of data. Answer: teenagers: 5 hr; twenties: 12 hr Answer: teenagers: 21 hours; twenties: 28 hours. The hours for the twenties group vary more. Example 2-3e