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Frequency polygons are virtually similar to a histogram and are used to evaluate the data of two sets or display a cumulative frequency spectrum. It uses the concept of a line graph to display quantitative data.
Statistics is the gathering of data for an intended purpose. The analysis of every run for every ball in cricket will provide the statistics for this sport. Tables, graphs, pie charts, bar graphs, histograms, polygons, etc., are used to depict statistics visually.
Frequency polygons can be a visual method of quantitatively expressing the frequency of data. Let’s look at what frequency polygons are.
What are Frequency Polygons?
Frequency polygons are a type of graphic representation of data. There are various methods by which data can be visually represented, but frequency polygons happen to be among the most effective and most efficient.
The information on paper is separated and arranged in the form of tables, then plotted on graph paper. The plotted graph is also presented by bars to make it easier to grasp the stats and understand the distribution of frequency data in a more precise method.
Benefits of Frequency Polygons
The frequency polygons don’t just assist in making sure the data is separated and depicted, but they also help evaluate and compare the results more quickly.
They are easier to comprehend and provide an accurate picture of the distribution of information.
This process isn’t lengthy like some other methods. It becomes much easier if the techniques used to draw and present the data are understood.
Steps to Draw Frequency Polygons
The curve of the frequency polygon is drawn using an x-axis and a y-axis. Like a normal graph, the x-axis measures a data set, while the y-axis displays the frequency in each category. When plotting a frequency-polygon graph, the most crucial feature is the midpoint. This is known as “the class interval” or marks of class.
The frequency polygon graph can be drawn with or without using a histogram. To draw a histogram, draw rectangular bars on the class intervals. Then join the midpoints of these bars to create frequency polygons.
These are the steps for drawing a frequency graph without a histogram:
Record the intervals of every class with an x-axis and plot the curve along the y-axis.
Calculate each class interval’s midpoint, known as the class marks:
Midpoint = Lower class limit + Upper class limit / 2
After the class marks have been obtained, mark their location on the x-axis.
As the height represents the frequency, draw the frequency according to the class mark. The frequency must be plotted on the mark, not against the upper or lower limit.
After the points have been marked together, connect them using a long line similar to the line graph.
The curve created by this line segment will be known as the frequency polygon.
Example of Frequency Polygons
Here is an example to understand what frequency polygons are.
Question: Build a frequency polygon using the information below:
Test Scores | Frequency |
49.5-59.5 | 5 |
59.5-69.5 | 10 |
69.5-79.5 | 30 |
79.5-89.5 | 40 |
89.5-99.5 | 15 |
Answer: We must determine the cumulative frequency based on the given frequency.
Test Scores | Frequency | Cumulative Frequency |
49.5-59.5 | 5 | 5 |
59.5-69.5 | 10 | 15 |
69.5-79.5 | 30 | 45 |
79.5-89.5 | 40 | 85 |
89.5-99.5 | 15 | 100 |
Now, we will plot the marks for the class like 54.5, 64.5, 74.5, and so on up to 94.5. We will also trace the preceding and subsequent class marks to begin and finish the polygon, i.e., we draw 44.5 and 104.5.
Then, the frequencies that correspond to the class marks will be plotted on each mark in the class. As you can see below, this is logical since the frequencies for marks for classes 44.5, 104.5, and 104.5 are both zero and lie on the x-axis. The plot points are used solely to provide an unfinished form for the polygon.
Conclusion
Frequency polygons are a visual representation of data distribution that aids in understanding data by presenting it in a particular shape. Frequency polygons have a lot of similarities to histograms, but they are more useful when analysing two or more datasets. The graph primarily displays data on cumulative frequency distributions as an equilateral line graph. Drawing frequency polygons on graphs to solve related problems helps understand the concept better.
