Lesson 13-3 Range – the difference between the greatest and least data Example 1 Find Range Find the range for each set of data. a. The length in days of family vacations: 5, 9, 14, 11, 15, 7, and 10. The greatest value is 15 and the least value is 5. So, the range is 15 – 5 or 10. b. Playing Video Games Stem 2 3 4 Leaf 6779 014558 269 42 = 42 minutes The greatest value is 49 and the least value is 26. So, the range is 49 – 26 or 23. Quartiles – the values that divide the data into four equal parts Lower Quartile – the median of the lower half of a set of data Upper Quartile – the median of the upper half of a set of data Interquartile Range – the difference between the upper quartile and the lower quartile Example 2 Identify Measures of Variation The table shows the pounds of paper that differentPounds of Paper classrooms collected on the first day of a recycling drive. Find the6 11 3 18 7 5 13 9 measures of variation for the data. RECYCLING Step 1 Find the range. 18 – 3 or 15 pounds Step 2 Find the median and the upper and lower quartiles. Order the data from least to greatest. median lower quartile 3 5 6 7 5+6 2 or 5.5 9 7+ 9 2 or 8 upper quartile 11 13 18 11+ 13 or 12 2 The median is 8, the lower quartile is 5.5, and the upper quartile is 12. Outliers – when a data point is more than 1.5 times the value of the interquartile range beyond the quartiles. Example 3 Find Outliers ROLLER COASTERS Find any outliers in the data set. Step 1 Find the interquartile range. lower quartile median upper quartile 1, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10 8–6=2 Number of Roller Coasters Ridden 5 8 9 9 8 7 6 7 1 10 7 5 6 8 7 8 Step 2 Step 3 Multiply the interquartile range, 2, by 1.5. 2 1.5 = 3 Subtract 3 from the lower quartile and add 3 to the upper quartile. 63=3 8 + 3 = 11 The only outlier is 1 because it is less than 3. Example 4 Use Measures of Variation LAKES Use the measures of variation to describe Average Depth of Lakes the data at the right. Average Lake Find the measures of variation. The range is 149 – 12 or 137. The median is 72 The upper quartile is 86. The lower quartile is 19. The interquartile range is 86 19 or 67. Lake Victoria Lake Superior Lake Michigan Great Bear Lake Lake Ontario Lake Erie Lake Winnipeg Depth (m) 40 149 72 72 86 19 12 The spread of the data is 137 meters. The median is 72 meters. One fourth of the lakes have an average depth of 19 meters or less. One fourth of the lakes have an average depth of 86 meters or more. Half of the lakes have a depth in the interval 19-86 meters. Real-World Example 5 Measures of Variation MARRIAGE The ages at which men and women first get married are listed in the stem-and-leaf plot. a. What is the median age for each group? The median age for the men is 35. So, one half men getting married are younger than 35. Men 9 86332 9765540 62 1 of 4 03 = 30 years 1 2 3 4 5 6 Women 889 011359 247 1 36 7 23 = 23 years The median age for the women is 27. So, one half of women getting married are younger than 27. b. Compare the range of ages for the men and the women. The range for the men is 64 – 19 or 45 years and the range for the women is 67 – 18 or 49 years. So, the ages vary more for the women than the men. c. How does the outlier affect the measures of central tendency for the ages of the women? Calculate the mean, median, and range without the outlier, 67. mean: median: mode: without the outlier 18 + 18 + …+ 56 29.8 16 25 18, 21 with the outlier 18 + 18 + …+ 67 32.1 16 27 18, 21 The mean increased by 32.1 – 29.8, or 2.3, the median increased by 27 – 25 or 2, and the mode did not change.

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