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Histograms
Histograms
When it is not necessary to show every value the way a stem plot would do, a histogram is a useful graph. Histograms organize numerical data into ranges, but do not show the actual values. The histogram is a summary graph showing how many of the data points falling within various ranges. Even though a histogram looks similar to a bar graph, it is not the same. Histograms are for numerical data and each 'bar' covers a range of values. Each of these 'bars' is called a class or bin. Histograms are a great way to see the shape of a distribution and can be used even when working with a large set of data.
The width of the bins is the most important decision when constructing a histogram. The bins need to be of consistent width (i.e. all cover a range of 10, or 25, etc.). It is generally a good idea to try to have 7 to 15 bins. Start with the range and divide by 10. This will give you a rough idea of how wide to make your bins. From there it becomes a judgment call as to what is a reasonable bin width. For example, it really does not make any sense to count by 11.24 just because that is what the range divided by 10 is equal to. In such a case, it might make more sense to count by 10's or 12's depending on the specific data.
Example 1
Suppose that the test scores of 27 students were recorded. The scores were: 8, 12,17, 22, 24, 28, 31, 37, 37, 39, 40, 42, 43, 47, 48, 51, 57, 58, 59, 60, 65, 65, 74, 75, 84, 88, 91. The lowest score was an 8 and the highest was a 91. Construct a histogram.
TEST SCORES
Test score histogram. http://www.netmba.com
The bins in this example are [0 to 10); [10 to 20); etc. This means that zero up to, but not including, 10 are in the first bin (9.999 would be in bin #1, but 10 would be in bin #2).
You may be creating your histograms with paper and pencil. However, the graphing calculators are a great way to create histograms as well. It takes a little practice to learn how to adjust the windows, but you have the opportunity to try out different bin widths without needing to erase or start all over. Also, you may want to see how to create histograms in excel. When you use a graphing calculator to create your graphs, you should sketch what the calculator shows you. Your sketch should look similar to the graphing window shown, and will still need labels and titles.
Example 2
a) Construct a histogram to look at the distribution of acceptance rates for these U.S. Universities.
b) Describe your findings.
[Figure4]
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