Introduction | Duration | Predicting the Time Between Eruptions | References and Resources
Introduction
This
project explores the statistically interesting data on the duration of
eruptions and the time between eruptions of the Old Faithful geyser in
Yellowstone National Park. When Old Faithful erupts, it does so from about one
and a half minutes to five minutes. Park rangers have discovered that they can
use the duration of the eruption to predict the time the next eruption will
occur. In this project, we will examine some of the data.
As always in a statistical experiment, we must be very careful to define the variables in a clear and unambiguous way. An eruption begins when water first comes out and stays out of the geyser cone; this is known as the continuous water phase. The eruption ends when no more water is splashing out of the cone. Thus, the duration of the eruption is the time between the beginning of the eruption and the end. The time between eruptions is defined as the time between the beginning of one eruption and the beginning of the next eruption.
A problem that is almost always present in any statistical experiment is the difficulty of accurately measuring the variables.
1. Do you see any problems with the measurement of the duration and time between eruptions variables?
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Duration
The Duration Dataset gives the duration (in minutes) for 107 consecutive eruptions of Old Faithful.
2. Construct a frequency distribution and sketch the corresponding histogram of the duration data.
3. Run the interactive histogram of the duration data, written by
Webster West.
(NOTE: You must view this applet with a Java-enabled browser.)
Play with the histogram bin size, with the goal of understanding the underlying
data.
A distribution is bimodal when it has two modes. On a graph, a bimodal distribution has two "humps".
4. Does it appear that the distribution of durations of Old Faithful eruptions is bimodal?
Evidently, the bimodal character of the distribution is due to the fact that Old Faithful undergoes two different kinds of eruptions.
5. Read the article Time trouble for geyser: It's no longer Old Faithful from Volume 5.03 of Chance News. This article describes how the geyser is changing over time.
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Predicting the Time Between Eruptions
In spite of the changes over time, the behavior of Old Faithful can still be predicted with some accuracy. The prediction rule basically says that if an eruption is short then the time to the next eruption is about 55 minutes; if the eruption is long, the time to the next eruption is about 80 minutes. The following table (adapted from Jason Project VIII: Yellowstone National Park) gives the prediction model more precisely.
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Duration |
Predicted Time |
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1.5 |
51 |
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2.0 |
58 |
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2.5 |
65 |
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3.0 |
71 |
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3.5 |
76 |
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4.0 |
82 |
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4.5 |
89 |
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5.0 |
95 |
The Time Between Eruptions Dataset gives observed values of duration and waiting time (in minutes), taken during April and May, 1997. The source is Jason Project VIII: Yellowstone National Park.
7. Using the waiting time dataset and the table above, compute the predicted waiting times and compare with the actual waiting times.
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References and Resources
1. Jason Project > Jason Project VIII: Yellowstone National Park
2. Yellowstone National Park Homepage
3. Chance Project > Chance News > Volume 5.03
5. Texas A & M University
Statistics > Webster
West > Histogram Applet
(NOTE: You must view this applet with a Java-enabled browser.)
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