Learning Materials
Features
Discover
A frequency polygon is a graphical representation of a data set with frequency information. It is one of the most common statistical tools used to represent and analyse grouped statistical data.
Millions of flashcards designed to help you ace your studies
Sign up for freeWhat is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
What is Vaia?
How does Vaia help me study more efficiently?
Where can I find more explanations like this?
What's smart about Vaia's flashcards?
Can I create my own content on Vaia?
How does spaced repetition work in Vaia flashcards?
What can you do with flashcards in Vaia?
Is Vaia a science-based learning platform?
How do Vaia's smart learning plans support your exam prep?
Can you create your own study sets in Vaia?
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team Frequency Polygons Teachers
The use of a frequency polygon has been shown to be very useful for trend analysis and data recall.
Below is an example of a frequency polygon.
The value of the data point is plotted along the horizontal axis, and the frequency corresponding to each data point is plotted along the vertical axis. So from the above graph, we can deduce that for x = 10, frequency = 8. We will explore further nuances of frequency polygons later on.
Given a grouped frequency distribution, follow the following steps to draw the corresponding frequency polygon.
1) Find the class mark for each class interval of the frequency distribution. To make it easier, you can add another column to the frequency distribution to note down the class marks.
class mark = \(\frac{\text{upper limit + lower limit}}{2}\)
2) Plot the class marks along the horizontal axis and the frequencies along the vertical axis.
3) For each class mark, plot the frequency corresponding to that class on the graph.
4) Join all the plotted points in sequential order (connect the first point with the second, then the second to the third, and so on ...)
5) The resulting figure is the necessary frequency polygon.
Example
Draw the frequency polygon graph for the following frequency distribution:
Class | frequencies |
5-7 | 15 |
7-9 | 18 |
9-11 | 28 |
11-13 | 7 |
13-15 | 22 |
15-17 | 35 |
Solutions
First, let's find the class mark for each class. We can show the results in the following table:
Class | Class Mark | frequencies |
5-7 | 6 | 15 |
7-9 | 18 | |
9-11 | 10 | 28 |
11-13 | 12 | 7 |
13-15 | 14 | 22 |
15-17 | 16 | 35 |
Now that we have all the class marks and the corresponding frequencies, we can plot the points on the graph taking the class marks on the horizontal axis and the frequencies on the vertical axis.
The graph after plotting the requisite points, Nilabhro Datta - Vaia originals
Finally, we have to join the plotted points sequentially.
The final frequency polygon, Nilabhro Datta - Vaia originals
The above diagram is our final frequency polygon.
Here are a few things to be mindful of when creating your own frequency polygon:
Make sure you use the class mark and not the class limits to plot the graph.
Sometimes you may want to obtain a closed polygon. In such cases, you could extrapolate the classes to the expected next class in either direction and consider the frequency of each class to be 0. In the above example, this would mean adding the classes (4, 0) and (18, 0) – since the expected next class mark on the left-hand side is 4 and on the right-hand side is 0.
Frequency polygons share many similarities with Histograms. Both histograms and frequency polygons are used to graphically represent frequency distribution. While frequency polygons can be drawn with or without a corresponding histogram, it is very easy to obtain a frequency polygon from a given histogram.
To draw a frequency polygon from a given histogram, join the middle of the top of each bar of the histogram sequentially.
This is effectively equivalent to the same process that we followed to draw our frequency polygon. The horizontal middle of the bar of a histogram is the class mark, and the top of the histogram is the corresponding frequency. Thus the middle of the top of each bar gives the point to plot on the graph, and by joining these points we get the frequency polygon.
Example
Frequency polygon from a histogram. Image: ECDC CC BY 4.0
In the above example, the frequency polygon is obtained by joining the middle of the top of each bar of the histogram sequentially.
A frequency polygon is a graphical representation of a data set with frequency information. It is one of the most common statistical tools used to represent and analyse grouped statistical data.
To draw a frequency polygon from a given grouped frequency distribution, we must plot the frequency against the class marks and not the class boundaries.
While frequency polygons can be drawn with or without a corresponding histogram, it is very easy to obtain a frequency polygon from a given histogram.
Sign up for free to gain access to all our flashcards.
What is a frequency polygon?
A frequency polygon is a graphical representation of a data set with frequency information. It is one of the most commonly used statistical tools used to represent and analyse grouped statistical data.
How to draw a frequency polygon?
To draw a frequency polygon, follow the following steps:
1) Find the class mark for each class interval of the frequency distribution.
Class mark = (upper limit + lower limit)/2
2) Plot the class marks along the horizontal axis and the frequencies along the vertical axis.
3) For each class mark, plot the frequency corresponding to that class on the graph.
4) Join all the plotted points in sequential order (connect the first point with the second, then the second to the third, and so on…)
5) The resulting figure is the necessary frequency polygon.
What is a frequency polygon used for?
A frequency polygon is one of the most commonly used statistical tools used to represent and analyze grouped statistical data. The use of a frequency polygon has been shown to be very useful for trend analysis and data recall.
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
Vaia is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of Vaia.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App 
