A geyser is a hot spring that occasionally becomes unstable and erupts hot water and steam into the air. The Old Faithful Geyser at Yellowstone National Park in Wyoming is probably the most famous geyser in the world. Visitors to the park try to arrive at the geyser site to see it erupt without waiting too long; the name of the geyser comes from the fact that eruptions follow a relatively stable pattern. The National Park Service erects a sign at the geyser predicting when the next eruption will occur, and also post these predic- tions at the Old Faithful Geyser WebCam page, which also includes a photo of the geyser that is updated roughly every 30 seconds. The histogram below is for a sample of 222 intereruption times taken during August 1978 and August 1979.

Instructions:
  1. Change the bin width from 10 to 15 and press Enter on your keyboard. How would you describe the shape of this distribution? What what you consider a typical wait time?
  2. Change the bin with to 10 (either by entering the value or by using the slider). How would you describe the shape of this distribution? What what you consider a typical wait time?
  3. Change the bin with to 5 (either by entering the value or by using the slider). How would you describe the shape of this distribution? What what you consider a typical wait time?

Moral: It's important to choose a bin width that is not too large as that could hide some important features of the distribution. Although a bin width that's too small could make it harder to see the overall pattern.

The histogram shows that, in fact, Old Faithful isn’t as “faithful” as you might think: times between eruptions range between 40 and 100 minutes, with two apparent subgroups in the data (in fact, the geyser has become so popular not because it is the largest or most regular geyser in Yellowstone Park, but rather because it erupts more frequently than any of the other large geysers in the park).