Question 3.38: Speeds of Roller Coasters The data shown are the speeds in m......
Speeds of Roller Coasters
The data shown are the speeds in miles per hour of a sample of wooden roller coasters and a sample of steel roller coasters. Compare the distributions by using boxplots.
| Wood | Steel | ||||||
| 50 | 56 | 60 | 48 | 55 | 70 | 48 | 28 |
| 35 | 67 | 72 | 68 | 100 | 106 | 102 | 120 |
Source: UltimateRollerCoaster.com
Step 1 For the wooden coasters,
\begin{aligned}& \begin{array}{llllllll}35 & 48 & 50 & 56 & 60 & 67 & 68 & 72\end{array} \\& \begin{array}{ccc}&&&\uparrow && \uparrow &&& \uparrow \\&&&Q_1 && \operatorname{MD} &&& Q_3\end{array} \\\end{aligned}
Q_1=\frac{48+50}{2}=49 \qquad \mathrm{MD}=\frac{56+60}{2}=58 \qquad Q_3=\frac{67+68}{2}=67.5
Step 2 For the steel coasters,
\begin{aligned} & \begin{array}{llllllll} 28 & 48 & 55 & 70 & 100 & 102 & 106 & 120 \end{array} \\ & \begin{array}{lll} &&\uparrow &&& \uparrow &&& \uparrow \\ && Q_1 &&& \mathrm{MD} &&& Q_3 \end{array}\end{aligned}
Q_1=\frac{48+55}{2}=51.5 \quad \mathrm{MD}=\frac{70+100}{2}=85 \quad Q_3=\frac{102+106}{2}=104
Step 3 Draw the boxplots. See Figure 3-8.
The boxplots show that the median of the speeds of the steel coasters is much higher than the median speeds of the wooden coasters. The interquartile range (spread) of the steel coasters is much larger than that of the wooden coasters. Finally, the range of the speeds of the steel coasters is larger than that of the wooden coasters.
