Frequency Polygon — Definition, Formula & Examples
A frequency polygon is a line graph made by plotting the frequency of each data group at its midpoint and then connecting the points with straight line segments.
A frequency polygon is a closed or open polygonal line constructed by plotting ordered pairs (class midpoint, frequency) for each class interval of a grouped frequency distribution and joining consecutive points with line segments. The graph is typically extended to the x-axis at both ends by adding points one class width before the first midpoint and one class width after the last midpoint, each with a frequency of zero.
Key Formula
Where:
- = The smallest value in the class interval
- = The largest value in the class interval
How It Works
Start with a frequency table that groups your data into equal-width intervals. Find the midpoint of each interval by averaging its lower and upper boundaries. Plot each midpoint on the x-axis against its frequency on the y-axis. Connect the plotted points in order with straight line segments. To close the polygon, add a point at frequency zero one class width before the first midpoint and one class width after the last midpoint, then connect those as well.
Worked Example
Problem: A teacher records quiz scores (out of 50) for 30 students and groups them into intervals: 1–10, 11–20, 21–30, 31–40, 41–50 with frequencies 3, 5, 10, 8, 4. Draw the key points of a frequency polygon.
Find midpoints: Calculate the midpoint of each interval.
List the points to plot: Pair each midpoint with its frequency: (5.5, 3), (15.5, 5), (25.5, 10), (35.5, 8), (45.5, 4).
Add closing points: The class width is 10. Add a zero-frequency point one width before the first midpoint and one width after the last midpoint.
Answer: Plot all seven points in order and connect them with straight line segments to form the frequency polygon.
Visualization
Why It Matters
Frequency polygons let you see the overall shape of a data distribution at a glance — whether it is skewed, symmetric, or has multiple peaks. They are especially handy when you need to compare two datasets on the same axes, since overlapping histograms can be hard to read.
Common Mistakes
Mistake: Plotting frequencies at the interval boundaries instead of the midpoints.
Correction: Always calculate the midpoint of each class interval. The midpoint represents the center of the group and is where the frequency should be plotted.