Recall the histogram demo from the last chapter, in which you could vary the bin size by dragging a slider--the shape of the histogram changes drastically as you change the size of the bin.
Why?
Play with the histogram again, this time with the goal of understanding the nature of the underlying data.
Here are some notes on the Old Faithful data and some possible reasons for the shape of its distribution.
There is a reason for calling the geyser 'Old Faithful'--its behavior can
be predicted. However, there is evidence that the geyser is not as faithful
as once thought. Here is an article about how
the geyser is changing over time.
Note that you will have to scroll down a bit to see the menu of choices: the story is number four in the list.
A distribution is bimodal when it has two modes. On a graph, a bimodal distribution has two 'humps'. Would you say the Old Faithful data is bimodal? The researchers apparently believe so--there are two different kinds of eruptions going on. Their prediction rule says that if you see a short eruption (represented by the first, left-most hump in the graph), the time to the next eruption is about 55 minutes. If you see a long eruption (represented by the second, right-most hump in the graph), the time to the next eruption is about 80 minutes.
Histograms show distributions. Distributions help explain something about the overall picture of the data. In this case, you see two humps in a distribution and find out something about how this geyser operates.
There is a reason why the distribution is two-humped, or bimodal, and it has to do with physics. This description of geysers provides a section on the 'plumbing' involved in geysers and a probable explanation of the mechanism at work deep inside 'Old Faithful'.
The following charts, graphs, and tables present a picture of wages and salary distributions for several different occupations. For the first two, you see a numeric table that shows the distribution. Can you look at the numbers and visualize how the histogram would appear?
In the charts for the CEOs, how does the shape of the age distribution differ from the wage distribution?
The way you look at data can have striking results in the conclusions you draw.
Some social commentators have noted that an increasing number of university graduates are taking jobs that require only high school diplomas. This, if true, results in a paradox when you also consider that the wages for university graduates is rising. If the graduates are working at low paying jobs, how can their wages be on the increase? This summary provides a resolution to the seeming paradox.