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# Frequency Polygons

## Constructing a graph connecting points of frequency for each interval.

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Frequency Polygons

A frequency polygon is closely related to a histogram. In fact, the difference is really only in the actual construction of the graph. Whereas a histogram is built of bins with a width representing the interval, and a height representing the quantity of data points in each interval, a frequency polygon is constructed by drawing a point to represent the frequency of a particular interval and connecting that point to the one representing the frequency of the next interval. The result is a shape very much like a histogram constructed from the same data, but with points instead of columns.

There are two common varieties of frequency polygon: absolute frequency and relative frequencyThe difference between them is how the frequency is counted. An absolute frequency polygon has ‘peaks’ that represent the actual number of points in the associated interval. A relative frequency polygon has peaks that represent the percentage of total data points falling within the interval.

To create an absolute frequency polygon:

1. Construct a frame just as you would for a histogram.
2. Label the vertical axis with the range of frequencies to be graphed, and the horizontal axis with the intervals you have chosen. Make your horizontal axis long enough to include a full interval above and below your graphed data so that the finished polygon has a visible starting and ending point.
3. Sum the number of points in each interval and mark a point representing the sum along the midline of the interval. The midline is on the arithmetic mean of the each interval, and can be calculated by adding the lower and upper limits of each interval and dividing the sum by two.
4. Once all points have been accounted for, connect the points and color in the area under the line.
5. If you are graphing a second set of data, repeat the process.

To construct a relative frequency polygon:

1. Construct a frame just as you would for a histogram.
2. Label the vertical axis from 0 – 100%, and the horizontal axis with the intervals you have chosen.
3. Sum the number of points in each interval, divide the sum of each interval by the total number of data points, and multiply by 100. The result is the percentage of the total number of data points that is represented by each interval. Mark a point representing the percentage along the midline of the interval.
4. Once all points have been accounted for, connect the points and color in the area under the line.
5. If you are graphing a second set of data, repeat the process.

Here is an example of a frequency polygon: