Topic 1: Organizing Information Pictorially Using Charts and Graphs

 

Histograms show how the values of the quantitative variables are distributed. The data is grouped into classes, so a histogram is useful for visualizing the distribution of data.

It is important to note that the classes in a histogram are of equal width. Contrast this with a general bar chart, which does not have this requirement.

Here is a step-by-step procedure for constructing a histogram for quantitative variables:

Example 1.7:

The following table gives a list of the acceptance rate for applicants to twelve U.S. universities.
(Source: Time Almanac 2004)

College or Univeristy

Percent Accepted
Harvard University 11
Yale University 16
Princeton University 12
Johns Hopkins University 32
New York University 29
M. I. T. 16
Duke University 26
Carnegie Mellon University 36
George Washington University 49
Northwestern University 33
American University 72
Cornell University 31

First, choose the size of the classes. Since the data values range from 11 to 72, if we choose classes 10 units wide, we will have seven different classes: 10 to 19, 20 to 29, 30 to 39, and so on. Then, count the number of data values in each class.

Class

Number of Universities
10 to 19 4
20 to 29 2
30 to 39 4
40 to 49 1
50 to 59 0
60 to 69 0
70 to 79 1

 

Finally, create the graph with seven adjacent bars, one for each class:

Note that in this example, all the data values were integers. In other problems with non-integral data, we must label the classes unambiguously so that every real number is in one class.


A stemplot (also called a stem-and-leaf graph) is another way to display a quantitative variable, especially if the data set is not too large.


Example 1.10:

Using the data from Example 1.7, we get the stemplot:
1 | 1 2 6 6
2 | 6 9
3 | 1 2 3 6
4 | 9
5 |
6 |
7 | 2