Frequency Polygons - Definitions, Steps, Formula, Example (2024)

Frequency polygons are a graphical representation of data distribution that helps in understanding the data through a specific shape. Frequency polygons are very similar to histograms but are helpful and useful while comparing two or more data. The graph mainly showcases cumulative frequency distribution data in the form of a line graph. Let us learn about the frequency polygons graph, the steps in creating a graph, and solve a few examples to understand the concept better.

Definition of Frequency Polygons

Frequency Polygons can be defined as a form of a graph that interprets information or data that is widely used in statistics. This visual form of data representation helps in depicting the shape and trend of the data in an organized and systematic manner. Frequency polygons through the shape of the graph depict the number of occurrence of class intervals. This type of graph is usually drawn with a histogram but can be drawn without a histogram as well. While a histogram is a graph with rectangular bars without spaces, a frequency polygon graph is a line graph that represents cumulative frequency distribution data. Frequency polygons look like the image below:

Steps to Construct Frequency Polygons

The curve in a frequency polygon is drawn on an x-axis and y-axis. As a regular graph, the x-axis represents the value in a dataset and the y-axis shows the number of occurrences of each category. While plotting a frequency polygon graph, the most important aspect is the mid-point which is called the class interval or class marks. The frequency polygon curve can be drawn with or without a histogram. For drawing with a histogram, we first draw rectangular bars against the class intervals and join the midpoints of the bars to get the frequency polygons. Here are the steps to drawing a frequency polygon graph without a histogram:

• Step 1: Mark the class intervals for each class on an x-axis while we plot the curve on the y-axis.
• Step 2: Calculate the midpoint of each of the class intervals which is the classmarks. (The formula is mentioned in the next section)
• Step 3: Once the classmarks are obtained, mark them on the x-axis.
• Step 4: Since the height always depicts the frequency, plot the frequency according to each class mark. It should be plotted against the classmark itself and not on the upper or lower limit.
• Step 5: Once the points are marked, join them with a line segment similar to a line graph.
• Step 6: The curve that is obtained by this line segment is the frequency polygon.

Formula to Find the Frequency Polygons Midpoint

While plotting a frequency polygon graph we require to calculate the midpoint or the classmark for each of the class intervals. The formula to do so is:

Class Mark (Midpoint) = (Upper Limit + Lower Limit) / 2

Difference Between Frequency Polygons and Histogram

Even though a frequency polygon graph is similar to a histogram and can be plotted with or without a histogram, the two graphs are yet different from each other. The two graphs have their own unique properties that show the difference visually. The differences are:

Related Topics

Listed below are a few topics that are related to frequency polygons, take a look.

• Line Chart
• Bar Graph
• Frequency Distribution

FAQs on Frequency Polygons

What is Frequency Polygons?

A frequency polygon is a type of line graph where the class frequency is plotted against the class midpoint and the points are joined by a line segment creating a curve. The curve can be drawn with and without a histogram. A frequency polygon graph helps in depicting the highs and lows of frequency distribution data. To obtain the curve for a frequency polygon, we need to find the classmark or midpoint from the class intervals.

How Do You Construct a Frequency Polygons?

A frequency polygon can be constructed with and without a histogram. The steps to construct a frequency polygon without a histogram are:

• Mark the class intervals for each class on an x-axis while we plot the curve on the y-axis.
• Calculate the midpoint of each of the class intervals which is the classmarks.
• Mark the classmarks on the x-axis.
• Since the height always depicts the frequency, plot the frequency according to each class mark. It should be plotted against the classmark itself and not on the upper or lower limit.
• Once the points are marked, join them with a line segment similar to a line graph.
• The curve that is obtained by this line segment is the frequency polygon.

What is the Difference Between Histogram and Frequency Polygons?

A frequency polygon graph is the improved version of a histogram. A histogram is a bar graph with rectangle-shaped bars depicting the data whereas a frequency polygon is a line graph where a curved line depicts the data. A frequency polygon is more widely used when distributive data needs to be compared since in a histogram the comparison will not be clear.

Why Do We Use Frequency Polygons?

Frequency polygons graphs are used in comparing a set of data as it is clear and more readable. These graphs are also widely used for depicting cumulative frequency distribution.

What are the Characteristics of Frequency Polygons?

A frequency polygon graph is considered as a closed dimensional figure of a line segment joining the midpoints of the given class intervals. The graph can either be drawn with a histogram or without a histogram. The first point is on the x-axis where y = 0 and is placed in the middle of the interval which precedes the first class interval.

What is the Similarity Between Frequency Polygons and Line Graphs?

A frequency polygon is a type of line graph where a line segment curves to join the midpoints of all the class intervals. The shape of the curved line helps in providing accurate data. Both a line graph and frequency polygon graph are widely used when data is required to be compared.