Frequency polygons are the graphical depiction of data distribution that uses a certain form to better comprehend the data. Frequency polygons are similar to histograms in appearance, but they are more useful for comparing two or more data sets. In the form of a line graph, the graph primarily displays cumulative frequency distribution data.

DEFINITION:-

Frequency Polygons are the type of graph that interprets some information or data and are frequently employed in statistics. This visual representation of data aids in the depiction of the data’s shape and trend in an ordered and systematic manner. The number of occurrences of class intervals is represented by frequency polygons that run the length of the graph. This style of the graph is typically drawn with a histogram, but it can also be drawn without one.

A frequency polygon graph is a line graph that represents cumulative frequency distribution data, whereas a histogram is a graph with rectangular bars without spaces.

Before constructing the frequency polygons here are some of the terminology that we should know about them:-

1. Class- interval:- It is vital for the observer to choose a suitable class interval. A class interval is just a range of values within which the data will fall. This should make the information appear basic and straightforward.
2. Mid-point:- This is the center point of the bar that will be produced for the data, and it must be identified for the graph’s symmetry.
3. Class-mark:- It’s nothing more than a point in the middle. It is the average of the class interval’s upper and lower limits.
4. Upper-limit:- The class interval’s upper limit is the class interval’s final boundary condition.
5. Lower- limit:- The class interval’s starting boundary condition is the lower limit.

HOW TO CONSTRUCT FREQUENCY POLYGONS:-

An x-axis and a y-axis are used to draw the curve in a frequency polygon. The x-axis indicates the value in a dataset, while the y-axis shows the number of occurrences of each category, as in a standard graph. The mid-point, also known as the class interval or class marks, is the most crucial factor to consider when plotting a frequency polygon graph. A histogram or no histogram can be used to draw the frequency polygon curve.

To create a frequency polygon with a histogram, we first draw rectangular bars against the class intervals and then link the midpoints of the bars. The steps for producing a frequency polygon graph without a histogram are as follows:

Step 1:-  On an x-axis, mark the class intervals for each class while plotting the curve on the y-axis.

Step 2:-  Find out the classmarks, which are the midpoints of each of the class intervals i.e. the mean of the upper height and the lower height.

Step 3:- After getting the classmarks, put them on the x-axis.

Step 4:-  Plot the frequency according to the respective class mark, since the height always indicates the frequency. It should be plotted with respect to the actual classmark, not the maximum or lower limit.

Step 5: After we have marked all of our points, connect them with a line segment as same as a line graph.

Step 6:- And then we get the frequency polygon curve that is the line segment that was connected to the points.

Benefits of frequency polygons:-

Here are some of the advantages of the frequency polygon that are listed below:-

• The frequency polygons will not only assist in sorting and representing the data, but they will also make it easier for individuals to compare and contrast all of the results.
• These are much simpler to comprehend and provide a clear picture of data distribution. It is vital for individuals to be able to read these graphs in order to comprehend them.
• This procedure isn’t even as time-consuming as some other processes. This gets easier if the techniques used to draw and portray the data are understood.

Important points:-

When creating a frequency polygon, keep the following considerations in mind:-

• Joining points on frequency polygons should be drawn in a straight line.
• Make sure to stay away from free-hand curves and rectangles. 
• Frequency polygons show the data that is being represented on the graph in a clear way. 
• One of the simplest methods for organizing data is to use a frequency polygon. It’s a means of displaying quantitative data and its frequency in a visual style. 
• It’s used to compare two sets of data or to depict a cumulative frequency distribution. For each interval, the formula for determining Classmark is 

CONCLUSION:-

One sort of graphical representation of data is frequency polygons. There are several ways to graphically display data, but frequency polygons are the best and most efficient of them all. A frequency polygon is very similar to a histogram, which is used to compare data sets or illustrate a cumulative frequency distribution. It represents quantitative data with a line graph.

The data of the specified class interval is represented by the precise points in a frequency polygon graph. In a frequency polygon graph, data comparison is more visually accurate.