3 4 BoxandWhisker Plots In the Real World

3. 4 Box-and-Whisker Plots In the Real World Roller Coasters The heights, in feet, of suspended roller coasters in the United States are given below. How can the data be displayed so that it is divided into quarters? 35 42 42. 5 60 60 70 76 78 81 100

3. 4 Box-and-Whisker Plots In the Real World Roller Coasters The heights, in feet, of suspended roller coasters in the United States are given below. How can the data be displayed so that it is divided into quarters? 35 42 42. 5 60 60 70 76 78 81 100 A box-and-whisker plot is a data display that divides data values into four parts. Ordered data are divided into a lower and an upper half by the median. The median of the lower half is the lower quartile. The median of the upper half is the upper quartile. The lower extreme is the least data value. The upper extreme is the greatest data value.

Box-and-Whisker Plots 3. 4 EXAMPLE 1 Making a Box-and-Whisker Plot To a box-and-whisker of themedian, roller coaster Plotmake the lower extreme, lowerplot quartile, upperheights quartile, given and above, first find the median. find the upper extreme using Then a number line. lower and upper quartiles. 30 60 + 70 Median = ––––––– = 65 50 60 70 2 80 90 40 • Lower half 35 42. 5 65 35 42 42. 5 60 60 Draw a box from the lower quartile to the upper quartile. Then draw a vertical line = 42. 5 Lower quartile through the median. 100 110 • Upper half 78 70 76 78 100 81 100 Draw a horizontal line from the box to each of Upper quartile 78 the = extremes.

3. 4 Box-and-Whisker Plots Interpreting a Box-and-Whisker Plot A box-and-whisker plot helps to show varied, or spread out, the data are. The large box represents about half of the data. Each small box represents about one quarter of the data. • • Each whisker represents about one quarter of the data. •

3. 4 EXAMPLE Box-and-Whisker Plots 2 Interpreting a Box-and-Whisker Plot Watches The prices of the watches at a store are displayed in the box-and-whisker plot below. 10 30 • • • 16 31 45 50 70 • 71 90 110 • 130 120 If all of the watches from under$31 $31 toare $71 on are clearance, on sale, then about what fraction of of the watches are on sale? clearance? SOLUTION The watches between less than$31 $31 and are $71 about arethe about same theassame the number as the number in one in the large of thebox whiskers, of the plot, which represents about one quarter half of the watches.

3. 4 EXAMPLE Box-and-Whisker Plots 3 Comparing Box-and-Whisker Plots Football The box-and-whisker plots forthcoming represent the number of points scored in each game of the 2001 -2002 season for the New England Patriots and 0 10 20 30 40 50 the St. Louis Rams. What conclusions can you make about. New the England data? • • • 3 St. Louis Rams 17 • 15 • 20. 5 31. 5 • 25. 5 • • 32. 5 36. 5 • 44 Patriots • 48 SOLUTION In general, the Rams scored more points per game than the Patriots. There is more variability in the points scored by the Patriots than by the Rams, with the range for the Patriots being 44 – 3 = 41 and the range for the Rams being 48 – 15 = 33.