10 4 Variability and BoxandWhisker Plots Warm Up
10 -4 Variability and Box-and-Whisker Plots Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
10 -4 Variability and Box-and-Whisker Plots Warm Up 1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92. 79, 87, 88, 89, 91, 92, 93 2. Find the median of the test scores. 89 Find the difference. 3. 17 – 0. 9 16. 1 4. 8. 4 – 7. 6 0. 8 5. 9. 1 – 5. 7 3. 4 6. 190. 3 – 23. 4 166. 9
10 -4 Variability and Box-and-Whisker Plots Problem of the Day What are the possible values for x in the data set 22, 12, 33, 25, and x if the median is 25? any number greater than or equal to 25
10 -4 Variability and Box-and-Whisker Plots Sunshine State Standards MA. 8. S. 3. 1 …Construct…box-and-whisker plots…to convey information and make conjectures about possible relationships.
10 -4 Variability and Box-and-Whisker Plots Vocabulary variability box-and-whisker plot first quartile third quartile interquartile range
10 -4 Variability and Box-and-Whisker Plots While central tendency describes the middle of a data set, variability describes how spread out the data are. A box-and-whisker plot uses a number line to show data are distributed and to illustrate the variability of a data set. A box-and-whisker plot divides the data into four parts. The median, or second quartile, divides the data into a lower half and an upper half. The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.
10 -4 Variability and Box-and-Whisker Plots
10 -4 Variability and Box-and-Whisker Plots Additional Example 1: Making a Box-and-Whisker Plot Use the given data to make a box-and-whisker plot: 21, 25, 13, 17, 19, 21 Step 1: Order the data and find the least value, first quartile, median, third quartile, and greatest value. 13 15 17 19 19 21 21 25 least value: 13 first quartile: greatest value: 25 15 + 17 2 third quartile: = 16 median: 19 + 19 = 19 2 21 + 21 2 = 21
10 -4 Variability and Box-and-Whisker Plots Additional Example 1 Continued Step 2: Draw a number line and plot a point above each value from Step 1. least value 13 12 13 15 17 19 19 21 21 25 14 first median third quartile 19 16 21 16 18 20 22 greatest value 25 24 26 28
10 -4 Variability and Box-and-Whisker Plots Additional Example 1 Continued Step 3: Draw the box and whiskers. 13 15 17 19 19 21 21 25 12 14 16 18 20 22 24 26 28
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 1 A Use the given data to make a box-and-whisker plot. 31, 23, 35, 26, 24, 31, 29 23 25 20 22 24 26 28 30 32 35 34 36 38 40
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 1 B Use the given data to make a box-and-whisker plot. 57, 53, 52, 31, 48, 58, 64, 86, 54, 55 31 30 40 55 52 58 50 60 86 70 80 90
10 -4 Variability and Box-and-Whisker Plots The interquartile range of a data set is the difference between the third quartile and the first quartile. It represents the range of the middle half of the data.
10 -4 Variability and Box-and-Whisker Plots Additional Example 2: Using Interquartile Range to Identify Outliers Use interquartile range to identify any outliers. 75, 65, 78, 79, 76, 79, 72, 82 Step 1: Determine the first quartile, the third quartile, and the interquartile range. 65 72 75 76 78 79 79 82 Q 1: 73. 5 Q 3: 79 IQR: 79 – 73. 5 = 5. 5
10 -4 Variability and Box-and-Whisker Plots Additional Example 2 Continued Use interquartile range to identify any outliers. 75, 65, 78, 79, 76, 79, 72, 82 Step 2: Determine whethere is an outlier less than the first quartile. Q 1 – (1. 5 IQR) 73. 5 – (1. 5 5. 5) 73. 5 – 8. 25 = 65. 25 The least value in the data set is 65. This value is less than 65. 25.
10 -4 Variability and Box-and-Whisker Plots Additional Example 2 Continued Use interquartile range to identify any outliers. 75, 65, 78, 79, 76, 79, 72, 82 Step 3: Determine whethere is an outlier greater than the third quartile. Q 3 + (1. 5 IQR) 79 + (1. 5 5. 5) 79 + 8. 25 = 87. 25 The greatest value in the data set is 82. None of the values are greater than 87. 25.
10 -4 Variability and Box-and-Whisker Plots Additional Example 2 Continued Use interquartile range to identify any outliers. 75, 65, 78, 79, 76, 79, 72, 82 The data value 65 is an outlier.
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 2 A Use the interquartile range to identify any outliers. 25, 12, 31, 26, 27, 29, 32 12, 25, 26, 27, 29, 31, 32 Q 1: 25 Q 3: 31 IQR = 31 – 25 = 6 Q 1 – (1. 5 • IQR) = 25 – (1. 5)(6) = 25 – 9 = 16
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 2 A Continued Use the interquartile range to identify any outliers. 25, 12, 31, 26, 27, 29, 32 Q 3 + (1. 5 • IQR) = 31 + (1. 5)(6) = 31 + 9 = 40 12 is less than 16, so 12 is an outlier. No values are greater than 40, so there are no other outliers.
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 2 B Use the interquartile range to identify any outliers. 35, 46, 50, 32, 54, 40 32, 35, 40, 44, 46, 50, 54 Q 1: 35 Q 3: 50 IQR = 50 – 35 = 15 Q 1 – (1. 5 • IQR) = 35 – (1. 5)(15) = 35 – 22. 5 = 12. 5
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 2 B Continued Use the interquartile range to identify any outliers. 35, 46, 50, 32, 54, 40 Q 3 + (1. 5 • IQR) = 50 + (1. 5)(15) = 50 + 22. 5 = 72. 5 No values are less than 12. 5 or greater than 72. 5, so there are no outliers.
10 -4 Variability and Box-and-Whisker Plots Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Note: 57 is the first quartile and the median. These box-and-whisker plots compare the ages of the first ten U. S. presidents with the ages of the ten presidents from Dwight Eisenhower through George W. Bush when they took office.
10 -4 Variability and Box-and-Whisker Plots Additional Example 3 Continued Note: 57 is the first quartile and the median. A. Compare the medians and ranges. The median for the first ten presidents is slightly greater. The range for the last ten presidents from 1953 -2008 is greater.
10 -4 Variability and Box-and-Whisker Plots Additional Example 3 Continued Note: 57 is the first quartile and the median. B. Compare the interquartile ranges. The interquartile range is greater for the ten presidents from 1953 -2008.
10 -4 Variability and Box-and-Whisker Plots Check It Out: Example 3 Compare the interquartile ranges of the data sets in Example 3. For the first ten presidents: IQR = 61 – 57 = 4 For the ten presidents from 1953– 2008: IQR = 62 – 52 = 10 The interquartile range is greater for the ten presidents from 1953– 2008.
10 -4 Variability and Box-and-Whisker Plots Lesson Quizzes Standard Lesson Quiz for Student Response Systems
10 -4 Variability and Box-and-Whisker Plots Lesson Quiz: Part I Use the following data for problems 1 and 2. 91, 87, 98, 93, 89, 78, 94 1. Make a box-and-whisker plot. 78 87 91 94 98 2. Use the interquartile range to identify and outliers. none
10 -4 Variability and Box-and-Whisker Plots Lesson Quiz: Part II 3. Use the box-and-whisker plots to compare the medians and ranges of the data sets. Data set A has a greater median. Data set B has a greater range.
10 -4 Variability and Box-and-Whisker Plots Lesson Quiz for Student Response Systems 1. Identify the first and third quartiles for the given data set. 15, 45, 65, 75, 35, 55, 25 A. Q 1 = 15; Q 3 = 65 B. Q 1 = 25; Q 3 = 65 C. Q 1 = 15; Q 3 = 75 D. Q 1 = 25; Q 3 = 75
10 -4 Variability and Box-and-Whisker Plots Lesson Quiz for Student Response Systems 2. Identify a box-and-whisker plot for the given data. 42, 72, 65, 44, 52, 79, 68, 55, 60 A. B.
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