What Is a Frequency Polygon?
A frequency polygon is a line graph created by plotting the midpoints of each class interval against their frequencies and connecting the points with straight lines. The line is typically extended to the x-axis at both ends by adding zero-frequency points at the midpoints before the first and after the last class.
Frequency polygons are particularly useful for comparing two or more distributions on the same axes, as overlapping line graphs are clearer than overlapping histograms. They provide a smooth visual representation of the distribution shape.
How to Create One
- Calculate the midpoint of each class: midpoint = (lower + upper) / 2
- Plot each midpoint against its frequency
- Connect points with straight lines
- Extend to x-axis by adding (first_mid - width, 0) and (last_mid + width, 0)
Polygon vs Histogram
| Feature | Frequency Polygon | Histogram |
|---|---|---|
| Display | Line graph | Bar graph |
| Comparison | Easy to overlay | Hard to overlay |
| Area | Area under = total | Area under = total |
| Shape | Smooth outline | Stepped outline |
Uses
- Comparing distributions of different groups on the same axes
- Visualizing the shape (symmetry, skewness) of distributions
- Identifying modes and patterns in grouped data
- Transitional step toward understanding probability density curves
Frequently Asked Questions
Must class widths be equal?
For a standard frequency polygon, yes. Unequal class widths require using frequency density (frequency/width) instead of raw frequency for the y-axis to maintain a valid visual representation.
Why extend the line to the x-axis?
Extending to zero-frequency points at both ends closes the polygon and ensures the area under the curve equals the total frequency, analogous to a probability distribution curve.
Can frequency polygons show cumulative frequency?
Yes. A cumulative frequency polygon (ogive) plots cumulative frequencies against upper class boundaries rather than midpoints. The resulting S-shaped curve is useful for finding percentiles.