Main Idea and New Vocabulary Example 1: Construct a Box-and-Whisker Plot Example 2: Interpret Data Example 3: Interpret Data Example 4: Double-Box-and-Whisker Plots Lesson Menu

Display and interpret data in box-and-whisker plots. Main Idea/Vocabulary

Construct a Box-and-Whisker Plot FLYING The list below shows the speed, in miles per hour, of commercial airliners. Draw a box-and-whisker plot of the data. 540, 460, 520, 350, 500, 480, 475, 525, 450, 515 Step 1 Order the numbers from least to greatest. Then draw a number line that covers the range of the data. 350, 450, 460, 475, 480, 500, 515, 520, 525, 540 Example 1

Construct a Box-and-Whisker Plot Step 2 Find the median, the extremes, and the upper and lower quartiles. Mark these points above the number line. Example 1

Construct a Box-and-Whisker Plot Step 3 Check for outliers. The interquartile range is 520 – 460 or 60. 60 × 1.5 = 90 460 – 90 = 370 and 520 + 90 = 610 So, 350 is an outlier. Step 4 Draw the box so that it includes the quartile values. Draw a vertical line through the box at the median value. Extend the whiskers from each quartile to the extreme data points that are not outliers. Example 1

Construct a Box-and-Whisker Plot Answer: Example 1

DRIVING The list below shows the speed, in miles per hour, of several cars on a road. Draw a box-and-whisker plot of the data. 52, 44, 59, 45, 50, 47, 46, 52, 60, 48 A. B. C. D. Example 1 CYP

Answer: Half of the commercial airliners travel slower than 490 mph. Interpret Data FLYING The box-and-whisker plot below shows the speed, in miles per hour, of commercial airliners. Half of the commercial airliners travel slower than what speed? Answer: Half of the commercial airliners travel slower than 490 mph. Example 2

DRIVING The box-and-whisker plot below shows the speed, in miles per hour, of several cars on a road. Half of the drivers are driving faster than what speed? A. 35 mph B. 46 mph C. 49 mph D. 52 mph Example 2 CYP

Interpret Data FLYING The box-and-whisker plot below shows the speed, in miles per hour, of commercial airliners. What does the length of the box-and-whisker plot tell you about this data? Answer: There is an outlier at 350. If the left whisker extended to this point, then the left whisker would be long. This means that the speeds of the slowest 25% of the airliners are spread out. Example 3

A. Both whiskers are long, so the speeds are very spread out. DRIVING The box-and-whisker plot below shows the speed, in miles per hour, of several cars on a road. What does the length of the box-and-whisker plot tell you about this data? A. Both whiskers are long, so the speeds are very spread out. B. If the outlier is included, then the left whisker would be longer, so the speeds of the slower half of the cars are more spread out. C. The right whisker is longer so the speeds of the faster half of the cars are more spread out. D. The boxes are the same size, so all of the speeds are concentrated. Example 3 CYP

Double-Box-and-Whisker Plots WEATHER The double box-and-whisker plot below shows the average low temperatures for two months. Compare and contrast the range and variability of the low temperatures in July and October. Answer: The range of low temperatures for October varied by 20 degrees whereas for July they varied by 10 degrees. So the daily low temperature varied more in October than in July. Example 4

The double box-and-whisker plot shows the average number of miles John ran for two months. Compare and contrast the range and variability of the number of miles he ran in April and May. A. The range of the number of miles ran in April varied by 8 miles, whereas in May they varied by 7 miles. So, the number of miles John ran varied more in May than in April. B. The range of the number of miles ran in April varied by 8 miles, whereas in May they varied by 11 miles. So, the number of miles John ran varied more in April than in May. C. The range of the number of miles ran in April varied by 3 miles, whereas in May they varied by 4 miles. So, the number of miles John ran varied more in April than in May. D. The range of the number of miles ran in April varied by 7 miles, whereas in May they varied by 8 miles. So, the number of miles John ran varied more in May than in April. Example 4 CYP