Creating & Interpreting Frequency Polygons: Process & Examples

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  • 0:05 Frequency Polygons
  • 0:38 What Are Frequency Polygons?
  • 1:46 Creating Frequency Polygons
  • 4:30 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Frequency polygons can be used to analyze data sets in many different ways. They are also a great way to visualize and compare two sets of data. In this lesson, learn the uses and create a frequency polygon.

Frequency Polygons

Jessica and Sam are archery coaches at rival high schools. Jessica claims that her students can shoot more bull's-eyes overall than Sam's students. Sam says his students are the best archery students. Jessica says her students are the best archery students.

So, who's right? Sam and Jessica can use a frequency polygon to compare their data and see, once and for all, who has the best archery students. In this lesson, learn how frequency polygons are used in analyzing data and how to create a frequency polygon.

What Are Frequency Polygons?

A frequency polygon is a line graph created by joining all of the top points of a histogram. They are called polygons because the line the graph creates resembles half of a polygon.

Frequency polygons:

  • Show the shape of a distribution of data
  • Can be seen with or without the histogram bars
  • Have end points that lie on the x-axis
  • Can be used to compare two sets of data
  • Are best for comparisons of data that have the same sample size

Jessica and Sam have five students each. During the past two weeks, each student shot a total of ten arrows at a bull's-eye from varying distances. A frequency polygon can show the shape of a distribution of data. Sometimes, it is easier to visualize two sets of data side-by-side by using a frequency polygon. You can use a frequency polygon with or without a histogram, and you'll see examples of this later on.

This is a table showing how many arrows hit a bull's-eye at each distance:

Data table for example
table showing archery data

Since Jessica and Sam have the same number of arrows, they can compare their data using a frequency polygon.

Creating Frequency Polygons

Let's use Jessica and Sam's data to create a frequency polygon.

To create a frequency polygon, follow these steps:

  1. Create a histogram
  2. Find the midpoints for each bar on the histogram
  3. Place a point on the origin and at the end of the histogram
  4. Connect the points

Histogram for example
histogram of archery data

First, use the data to create a histogram. The horizontal, or the x-axis, shows the distances of each bull's-eye, while the vertical, or the y-axis, shows the number of arrows that struck each bull's-eye for Jessica and for Sam. The vertical axis is the frequency in the distribution of data. The frequency for Jessica's data is represented by the blue lines, and the frequency for Sam's data is represented by the orange lines.

Next, find the midpoints for each bar on the histogram. Mostly, you just want to make sure that the point lines up with the top center of the histogram so that there isn't any confusion about which frequency the point represents. The points for Jessica are in blue, and the points for Sam are in orange.

Then, place the points on the origin, or at 0,0 of the graph. This just shows the increase from nothing to the first frequency on the histogram. I've placed the points side-by-side on this graph so that you can see both points, but normally they would be directly on top of one another. You also need to place a point at the end of the histogram on the x-axis. This, again, represents zero frequencies for that side of the graph.

Graph showing point of origin and line connecting points with histogram bars
frequency polygon with histogram bars

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