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What Is A Frequency Polygon?

Gaining a better understanding of statistics.


There are lots of different ways to represent data collected from a scientific experiment, and organizing your recordings can be a fun task! The reason why we process our data in so many different ways is to make the results we obtain really mean something. It helps us to draw conclusions, make comparisons and simplify our results. One way of doing this is by making frequency polygons. Frequency polygons are very useful for comparing different sets of information on the same diagram, and it is a way of displaying grouped data. This might sound complicated, but it can be easy to get the hang of! Here we will go through how to construct frequency polygons in a few simple steps.


Displaying and presenting data is an important skill.


Data Presentation


The aim of creating different types of graphs and pictorials such as frequency polygons is to present our data. That is the key objective of statistics. Presenting data in different ways can help us to visualize information and give us a better understanding of the shapes and the trends that our findings have shown. This makes scientific information more recognizable so that it is easier to interpret at a quick glance. Presenting data can be done in many different ways such as bar charts, pie charts, histograms, and frequency polygons.


Frequency Polygons


A frequency polygon is a graphical way of displaying information. It is a great way to show the specific shape of the data collected and to depict trends. To draw a frequency polygon, it is easiest to use a histogram as an aid, but it can also be done without. Histograms and frequency polygons display the same data, but it is useful to know both. A histogram is a graph that displays data in a series of rectangular bars with no spaces in between them and is used to represent distribution frequency. In statistics, a frequency distribution is a list, table, or graph that displays the frequency of various outcomes in a sample. In the following steps, we will go over how to draw a frequency polygon without a histogram.


How To Draw A Frequency Polygon


Practice makes perfect.


To draw a frequency polygon, make sure that you have a pencil and paper ready (of course), but more importantly a ruler to keep everything as neat as possible. With a bit of practice you will surely get the hang of it with these simple steps:


  1. On the horizontal axis, mark the intervals for each class. On the vertical axis, we will be plotting the frequency.

  2. Now we need to figure out the classmark for each class interval. The classmark is also commonly known as the class midpoint. To calculate this we use the formula: class mark = (upper limit + lower limit) / 2

  3. Mark your calculated class marks on the horizontal axis.

  4. Now we can start plotting! Plot the frequency as given to you in correspondence to each class mark. The frequency is always depicted by the height, so make sure that that the frequency is plotted against the class mark and not the upper or lower limits of the classes.

  5. To join the plotted points, use a line segment. This means that the line you draw will be kinked instead of one smooth line.

  6. The curve that you have achieved is called the frequency polygon!


Note that if you have already drawn a histogram, you can also draw a frequency polygon on the same graph. This can be done by drawing a line that connects the midpoints of the tops of the rectangle bars on the histogram. So you may find it easier to first draw a histogram and then obtain the frequency polygon after by using this method.


Remember to try out plenty of examples to consolidate your learning.


What Are Frequency Polygons Useful For?


Now that you have drawn your frequency polygon, you may be wondering how you can interpret it and use it to make conclusions about the data you have shown. Frequency polygons can be particularly useful as you can now compare different sets of data on the same diagram. They can also help to do more complicated things like displaying cumulative frequency distributions.


Even though frequency polygons and histograms are similar in the information that they display, an advantage of using a frequency polygon is that it can directly compare multiple frequency distributions and shows the class midpoints at the same time.


In Summary


Here are some key points to take away from this guide:

  • A frequency polygon is a graph constructed by using lines to join the midpoints (or class mark) of each interval.

  • The heights of the midpoints represent the frequencies.

  • A frequency polygon can be created from the histogram or by calculating the midpoints of the intervals from the frequency distribution table.

  • The midpoint is calculated by adding the upper and lower boundary values of the interval and dividing the sum by 2.

  • Frequency polygons are useful for comparing different sets of data on the same diagram.


Keeping It Simple


Sometimes scientific data and statistics can all seem rather complicated and tricky to get your head around, but hopefully, these steps keep it simple and make it a little more understandable. When it comes to mathematics and data analysis, the key is practice, so keep at it and use plenty of examples to solidify your understanding! Once you get the hang of creating graphs like histograms and frequency polygons, it will become a useful skill to have in your mathematical toolbox.


Knowing how to display data and information comes in handy in many aspects of science, so not only is this important for you to know for your exams, but also for other aspects of your studies. You never know when you might need to whip up a quick frequency polygon for a biology or physics paper! Good luck and happy studying!


You may explore resources available on StudySquare for other helpful hints and tips for successfully navigating the world of maths and science. Specifically for frequency graphs visit:

https://www.studysquare.co.uk/test/Maths/AQA/GCSE/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/Edexcel/GCSE/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/OCR/GCSE/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/SQA/National-5/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/SQA/Higher/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/AQA/A-level/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/Edexcel/A-level/Graphs-and-plots

https://www.studysquare.co.uk/test/Maths/OCR/A-level/Graphs-and-plots



Lili Coutts is an independent writer studying for a Bachelor's Degree in Mathematics and Biology at the University of Edinburgh. She is particularly interested in statistics and genetics and is enthusiastic about giving helpful study advice.

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