A frequency polygon is a line graph used to show the shape of grouped data. It is built from the same information as a histogram, but instead of drawing bars, it connects points at the class midpoints. This makes patterns such as peaks, spread, and symmetry easier to see.
Frequency polygons matter because they help compare data distributions clearly on one set of axes.
To make a frequency polygon, find the midpoint of each class interval and plot it against that class frequency. Then connect the plotted points with straight line segments, usually adding zero-frequency points before the first class and after the last class to close the shape. A faint histogram behind the polygon can show how the line graph is related to the grouped data.
When two or more frequency polygons are drawn together, differences in center, variability, and overall shape become easier to compare.
Key Facts
- Class midpoint = (lower class limit + upper class limit) / 2
- A frequency polygon plots points in the form (class midpoint, frequency).
- Connect consecutive midpoint-frequency points with straight line segments.
- Add one zero-frequency point before the first class and one after the last class to bring the polygon down to the x-axis.
- A frequency polygon uses the same grouped data as a histogram, but it shows the distribution with a connected line.
- Frequency polygons are useful for comparing two or more distributions on the same coordinate axes.
Vocabulary
- Frequency polygon
- A frequency polygon is a line graph that displays grouped data by connecting class midpoint points plotted against their frequencies.
- Class interval
- A class interval is a range of values used to group data, such as 10 to 19 or 20 to 29.
- Class midpoint
- A class midpoint is the center value of a class interval, found by averaging the lower and upper class limits.
- Frequency
- Frequency is the number of data values that fall within a particular class interval.
- Histogram
- A histogram is a graph of grouped numerical data that uses adjacent bars to show frequencies for class intervals.
Common Mistakes to Avoid
- Plotting class limits instead of class midpoints is wrong because a frequency polygon represents each interval by its center point.
- Forgetting to add zero-frequency endpoints is wrong because the graph may look unfinished and may not show the distribution returning to the x-axis.
- Using unequal class widths without noting them is wrong because the visual shape can become misleading when intervals do not represent the same span of values.
- Connecting points out of order is wrong because the line must follow the classes from lowest midpoint to highest midpoint to show the distribution correctly.
Practice Questions
- 1 A grouped data table has class intervals 0 to 9, 10 to 19, 20 to 29, and 30 to 39 with frequencies 3, 8, 12, and 7. Find the class midpoint for each interval and list the points to plot for the frequency polygon.
- 2 For the classes 40 to 49, 50 to 59, 60 to 69, 70 to 79, and 80 to 89, the frequencies are 4, 10, 15, 9, and 2. Draw the frequency polygon, including zero-frequency endpoints.
- 3 Two frequency polygons are drawn on the same axes. Distribution A has one high peak near the middle and low frequencies at both ends, while Distribution B is flatter and spread across many midpoints. Explain which distribution has greater variability and why.