Statistics

Graphical Representation

The table shown above is one way of representing the frequency distribution of a sample or population. A frequency distribution is any method for summarizing data that shows the number of individuals or individual cases present in each given interval of measurement. In the table above, there are 5,382,025 female African-Americans in the age group 0-19; 2,982,305 in the age group 20-29; 2,587,550 in the age group 30-39; and so on.

A common method for expressing frequency distributions in an easy-to-read form is a graph. Among the kinds of graphs used for the display of data are histograms, bar graphs, and line graphs. A histogram is a graph that consists of solid bars without any space between them. The width of the bars corresponds to one of the variables being presented, and the height of the bars to a second variable. If we constructed a histogram based on the table shown above, the graph would have six bars, one for each of the six age groups included in the study. The height of the six bars would correspond to the frequency found for each group. The first bar (ages 0-19) would be nearly twice as high as the second (20-29) and third (30-39) bars since there are nearly twice as many individuals in the first group as in the second or third. The fourth, fifth, and six bars would be nearly the same height since there are about the same numbers of individuals in each of these three groups.

Another kind of graph that can be constructed from a histogram is a frequency polygon. A frequency polygon can be made by joining the midpoints of the top lines of each bar in a histogram to each other.