Chapter PI, Problem 19RE

(a)

To determine

To describe the distribution.

Explanation of Solution

In the question, researchers want out find out does the duration of the eruption have an effect on the length of time elapses before the next eruption. Thus, the histogram is given which shows the duration in minutes of those of $222$ eruptions. Thus, we can say that by looking at the histogram that the distribution is bimodal as we can see the most highest two bars in the histogram and the modes will be near $2\text{ and 4}\text{.5}$ minutes. The distribution is fairly symmetrical around each mode.

(b)

To determine

To explain why it is not appropriate to find the summary statistics for the distribution.

Explanation of Solution

In the question, researchers want out find out does the duration of the eruption have an effect on the length of time elapses before the next eruption. Thus, the histogram is given which shows the duration in minutes of those of $222$ eruptions. Thus, it is not appropriate to find the summary statistics for the distribution because there are two models which probably corresponds to two different groups of eruptions and average might not make sense.

(c)

To determine

To describe what you see in the comparative boxplots.

Explanation of Solution

In the question, researchers want out find out does the duration of the eruption have an effect on the length of time elapses before the next eruption. In the boxplot we can see that the intervals between eruptions are longer for long eruptions. There is very little overlap. It shows that more than $25\%$ of the short eruptions and intervals less than about an hour, while more than $75\%$ of the long eruptions had intervals longer than about $75$ minutes. Perhaps the interval could even be used to predict whether the next eruption will be long or short.