9-4 Variability Warm Up Problem of the Day Lesson Presentation Course 3 Warm Up Problem of the Day Lesson Presentation

Course 3 9-4 Variability Warm Up 1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92. 2. Find the median of the test scores. Find the difference. 79, 87, 88, 89, 91, 92, 93 89 3. 17 – 0.9 4. 8.4 – 7. 6 16.1 0.8 5. 9.1 – 5.7 6. 190.3 – 23.4 3.4 166.9

9-4 Variability Problem of the Day Course 3 9-4 Variability 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

Course 3 9-4 Variability Learn to find measures of variability.

Insert Lesson Title Here Course 3 9-4 Variability Insert Lesson Title Here Vocabulary variability quartile box-and-whisker plot

9-4 Variability Litter Size 2 3 4 5 6 Number of Litters 1 8 11 Course 3 9-4 Variability The table below summarizes a veterinarian’s records for kitten litters born in a given year. Litter Size 2 3 4 5 6 Number of Litters 1 8 11 While central tendency describes the middle of a data set, variability describes how spread out the data is. Quartiles divide a data set into four equal parts. The third quartile minus the first quartile is the range for the middle half of the data.

Course 3 9-4 Variability The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4. Kitten Data Lower half Upper half 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 First quartile: 3 median of lower half Median: 4 (second quartile) Third quartile: 5 median of upper half Litter Size 2 3 4 5 6 Number of Litters 1 8 11 The range is affected by outliers, so another measure is often used. Quartiles divide a data set into four equal parts. The third quartile minus the first quartile is the range for the middle half of the data.

Additional Example 1A: Finding Measures of Variability Course 3 9-4 Variability Additional Example 1A: Finding Measures of Variability Find the first and third quartiles for the data set. 15, 83, 75, 12, 19, 74, 21 12 15 19 21 74 75 83 Order the values. first quartile: 15 third quartile: 75

Additional Example 1B: Finding Measures of Variability Course 3 9-4 Variability Additional Example 1B: Finding Measures of Variability Find the first and third quartiles for the data set. 75, 61, 88, 79, 79, 99, 63, 77 61 63 75 77 79 79 88 99 Order the values. first quartile: = 69 63 + 75 2 third quartile: = 83.5 79 + 88 2

9-4 Variability Check It Out: Example 1A Course 3 9-4 Variability Check It Out: Example 1A Find the first and third quartiles for the data set. 25, 38, 66, 19, 91, 47, 13 13 19 25 38 47 66 91 Order the values. first quartile: 19 third quartile: 66

9-4 Variability Check It Out: Example 1B Course 3 9-4 Variability Check It Out: Example 1B Find the first and third quartiles for the data set. 45, 31, 59, 49, 49, 69, 33, 47 31 33 45 47 49 49 59 69 Order the values. first quartile: = 39 33 + 45 2 third quartile: = 54 49 + 59 2

Course 3 9-4 Variability A box-and-whisker plot shows the distribution of data. The middle half of the data is represented by a “box” with a vertical line at the median. The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the smallest and largest values. 1 2 3 4 5 6 7 8 9 Median First quartile Third quartile

Use the given data to make a box-and-whisker plot: Course 3 9-4 Variability Additional Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21 Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. 13 15 17 19 19 21 21 25 smallest value: 13 largest value: 25 first quartile: = 16 15 + 17 2 third quartile: = 21 21 + 21 2 median: = 19 19 + 19 2

Use the given data to make a box-and-whisker plot. Course 3 9-4 Variability Additional Example 2 Continued Use the given data to make a box-and-whisker plot. Step 2. Draw a number line and plot a point above each value from Step 1. 13 15 17 19 19 21 21 25 smallest value 13 first quartile 16 median 19 third quartile 21 largest value 25 12 14 16 18 20 22 24 26 28

Use the given data to make a box-and-whisker plot. Course 3 9-4 Variability Additional Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. 13 15 17 19 19 21 21 25 12 14 16 18 20 22 24 26 28

Use the given data to make a box-and-whisker plot. Course 3 9-4 Variability Check It Out: Example 2 Use the given data to make a box-and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29 Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. 23 24 26 29 31 31 33 35 smallest value: 23 largest value: 35 first quartile: = 25 24 + 26 2 third quartile: = 32 31 + 33 2 median: = 30 29 + 31 2

Use the given data to make a box-and-whisker plot. Course 3 9-4 Variability Check It Out: Example 2 Continued Use the given data to make a box-and-whisker plot. Step 2. Draw a number line and plot a point above each value. 23 24 26 29 31 31 33 35 22 24 26 28 30 32 34 36 38

Use the given data to make a box-and-whisker plot. Course 3 9-4 Variability Check It Out: Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. Step 2. Draw a number line and plot a point above each value. 23 24 26 29 31 31 33 35 22 24 26 28 30 32 34 36 38

Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Course 3 9-4 Variability 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 last ten presidents (through George W. Bush) when they took office.

Additional Example 3 Continued Course 3 9-4 Variability 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 is greater.

Additional Example 3 Continued Course 3 9-4 Variability Additional Example 3 Continued Note: 57 is the first quartile and the median. B. Compare the differences between the third quartile and first quartile for each. The difference between the third quartile and first quartile is the length of the box, which is greater for the last ten presidents.

9-4 Variability Check It Out: Example 3 Oakland Course 3 9-4 Variability Check It Out: Example 3 Final 1 2 3 4 T Oakland 6 12 21 Tampa Bay 17 14 48 Oakland 0 3 6 9 12 15 18 Tampa Bay These box-and-whisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters.

9-4 Variability Check It Out: Example 3A Course 3 9-4 Variability Check It Out: Example 3A Compare the medians and ranges. Oakland 0 3 6 9 12 15 18 Tampa Bay The median for Tampa Bay is significantly greater, however the range for Tampa Bay is slightly greater.

9-4 Variability Check It Out: Example 3B Course 3 9-4 Variability Check It Out: Example 3B Compare the differences between the third quartile and first quartile for each. Oakland 0 3 6 9 12 15 18 Tampa Bay The difference between the third quartile and first quartile is the length of the box, which is slightly greater for Oakland.

Insert Lesson Title Here Course 3 9-4 Variability Insert Lesson Title Here Lesson Quiz: Part I Find the first and third quartile for each data set. 1. 48, 52, 68, 32, 53, 47, 51 2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0 Q1 = 47; Q3 = 53 Q1 = 2.5; Q3 = 12

Insert Lesson Title Here Course 3 9-4 Variability Insert Lesson Title Here Lesson Quiz: Part II Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 94 3. Make a box-and-whisker plot 4. What is the mean? 78 87 91 94 98 90