The most famous geyser in Yellowstone, Old Faithful, taken at sunset.

A Little About Old Faithful

Old Faithful is a geyser that is found in Yellowstone National Park, in Wyoming. It is one of the most famous attractions at Yellowstone National Park. Old Faithful is unique because of how long and how often it erupts. The eruptions can be observed and recorded. Data recorded from 1990 measured the time between eruptions and the duration of the eruption, both taken in minutes. This data set was based on 272 observations of Old Faithful’s eruptions.

Summary of Data:

By looking at the scatter plot, we can see a visual representation of the data. If you are planning on visiting Old Faithful, on average, you are going to wait around 70.9 minutes to see it erupt for about 3.49 minutes. The information on the scatter plot would lead you to believe that seeing a eruption around 3.0 minutes would be rare. This is because there are two clusters of data, the first cluster is eruptions over 3.5 minutes and the second cluster is below 2.5 minutes. Very few eruptions are between 2.5 and 3.5 minutes so you are most likely to see an eruptions over 3.5 minutes or under 2.5 minutes. The time you wait will coincide with how long Old Faithful erupts. There is a , 0.90081, correlation between wait time and eruption time, this is very close to one. This means that the erutpion’s time depends on the time that you wait. Thus, if the geyser eruption is short in duration, the wait time will be shorter than if the geyser erupts for a longer time, on average. Your wait time will vary from 43 minutes to 96 minutes, so plan something to do while waiting for Old Faithful to erupt.

Frequency of the Data

The next graphs that are shown give the frequency of both eruption time and wait time for the next eruptions of Old Faithful. Then we will take a look at a chart of data where there is a minimal number of data points between the eruption times of 2.5 to 3.5 mintues.

Rare Eruptions
   eruptions waiting
1      2.617      53
2      2.633      65
3      2.800      56
4      2.883      55
5      2.900      63
6      3.067      69
7      3.317      83
8      3.333      74
9      3.333      68
10     3.367      66
11     3.417      64
12     3.450      78
13     3.500      66
14     3.500      87

Taking a look at the first histogram, the Frequency of the Eruption Duration, the high numbers of frequencies on the sides of the graph represent the clusters that showed up in the scatter plot. The boxplot to the right of the histogram plot provides another view of this. The horizontal black line is the average and the box in the graph represents 25% to 75% of the eruptions. The vertical lines stemming from the box show the lower and upper 25% of eruptions. The second histogram, Frequency of Time Waiting, shows a similar pattern. The clusters of high frequencies of wait times mimic a similar pattern as the Frequency of the Eruption Duration, with two clusters of data towards the middle-right and middle-left. There is a dip in wait time frequency between these two clusters. Looking to the right we can look at this information through a box plot. On the first histogram graph, there is a dip showing a low frequency of eruptions happening between 2.5 minutes and 3.5 minutes. Now looking at the Rare Eruption table you can see the eruptions that took place during this dip. Of the 272 observations, only 14 of the eruptions lasted between 2.5 minutes and 3.5 minutes.

Conclusion

Thus, when visiting Yellowstone National Park and going to see Old Faithful, you should set aside a morning or afternoon so you have enough time to see Old Faithful erupt a few times and hopefully get lucky to watch it erupt for a long time, making the wait worthwhile. Do not be discouraged if the wait time is long though, this will likely mean that the eruption that you see will last for a long time.