Variability 4.4 Pre-Algebra
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 0.8 166.9 3.4 5. 9.1 – 5.7 6. 190.3 – 23.4
Learn to find measures of variability.
Vocabulary variability range quartile box-and-whisker plot
Range and Quartiles The range of a data set is the largest value minus the smallest value. The table below summarizes a veterinarian’s records for kitten litters born in a given year. 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.
Example: Finding Measures of Variability Find the range and the first and third quartiles for the data set. A. 15, 83, 75, 12, 19, 74, 21 Order the values. 12 15 19 21 74 75 83 range: 83 – 12 = 71 first quartile: 15 third quartile: 75
63 + 75 2 first quartile: = 69 79 + 88 2 third quartile: = 83.5 Example: Finding Measures of Variability Find the range and the first and third quartiles for the data set. B. 75, 61, 88, 79, 79, 99, 63, 77 Order the values. 61 63 75 77 79 79 88 99 range: 99 – 61 = 38
Try This Find the range and the first and third quartiles for the data set. A. 25, 38, 66, 19, 91, 47, 13 Order the values. 13 19 25 38 47 66 91 range: 91 – 13 = 78 first quartile: 19 third quartile: 66
33 + 45 2 first quartile: = 39 49 + 59 2 third quartile: = 54 Try This Find the range and the first and third quartiles for the data set. B. 45, 31, 59, 49, 49, 69, 33, 47 Order the values. 31 33 45 47 49 49 59 69 range: 69 – 31 = 38
1 2 3 4 5 6 7 8 9 Box-and-Whisker Plot 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. Median First quartile Third quartile
15 + 17 2 21 + 21 2 third quartile: = 21 first quartile: = 16 19 + 19 2 median: = 19 Example: 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
12 14 16 18 20 22 24 26 28 Example Continued Use the given data to make a box-and-whisker plot. Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. 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 third quartile 21 largest value 25 median 19
12 14 16 18 20 22 24 26 28 Example 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. Step 3. Draw the box and whiskers. 13 15 17 19 19 21 21 25
31 + 33 2 24 + 26 2 third quartile: = 32 first quartile: = 25 29 + 31 2 median: = 30 Try This 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
22 24 26 28 30 32 34 36 38 Try This 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 Try This 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. Step 3. Draw the box and whiskers. 23 24 26 29 31 31 33 35
Example: 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.
Example 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.
Example 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.
Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18 Try This 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.
Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18 Try This Continued A. Compare the medians and ranges. The median for Tampa Bay is significantly greater, however the range for Tampa Bay is slightly greater.
Oakland 0 3 6 9 12 15 18 Tampa Bay 0 3 6 9 12 15 18 Try This Continued 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 slightly greater for Oakland.
Lesson Quiz: Part 1 Find the range and 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 range = 36; Q1 = 47; Q3 = 53 range = 18; Q1 = 2.5; Q3 = 12
78 87 91 94 98 Lesson Quiz: Part 2 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? 90
