Cumulative frequency graphs allow us to graphically represent the cumulative total of frequencies. By interpreting cumulative frequency graphs, we cannot only find information about the data such as the media but also predict sets of additional data.
Creating Cumulative Frequency Graphs
To create a cumulative frequency graph, you need a table with data such as the one underneath. It usually has to contain some ranges of values (the marks in this case) and the frequency. You will have to calculate the cumulative frequency which are the frequencies added up. Now you can start plotting the graph. The cumulative frequency should always be on the y axis. To plot the data, just take the upper bound of each range (in the table these are written in bold) as the x value and the cumulative frequency as the y value. The last step is to draw a line connecting these points. The line should be curved in some places and go through every point. Lastly, you should check if the axes are labelled and if the graph has a title (if necessary). Now you can use the graph to find additional information.
Finding Information using Cumulative Frequency Graphs
Let us find the:•min value (estimated)By looking at the curve, we can see that the min value is at about 5% or 6%. To do this we just look at where a horizontal line going through y=1 cuts the curve. This value can vary depending on how the curve is drawn.•max value (estimated)By looking at the curve, we can see that the max value is at about 100%. To do this we just look at where a horizontal line going through y=45 cuts the curve. This value can vary depending on how the curve is drawn.•median (estimated)We can find the median by calculating half of the total cumulative frequency (22.5) and imagining a horizontal line passing through this point on the y axis. The x value of where this line cuts the curve is the median. In this case it is about 54.•lower & upper quartile (estimated)We can find the quartiles by finding 1/4 and 3/4 of the total cumulative frequency and then doing the same as we have done for the median. In this example, the lower quartile is approximately 42 and the upper quartile 65.By using common sense and looking at the cumulative frequency graph we can also make logical statements such as:•“The majority of students scored over 50%.”•“Only 5 students scored 80% or more.”•“4 students scored 20% or less.”
Next you should look at our histograms lesson. Histograms show the frequency as well as the distribution of data. Please share this page if you like it or found it helpful!
ULTIMATE MATHSBecoming an Accomplished MathematicianUltimate Maths is a professional maths website that gives students the opportunity to learn, revise and apply different maths skills. We provide a wide range of lessons and resources...
ContactGet in touch by using the Contact Us button.
Stay UpdatedVisit our Forum & Blogto stay updated about the latest Ultimate Maths News
Quality ContentA wide range of quality learning resources is at your disposal.
Effective TeachingExplanations, examples and questions combined for an effective learning experience.
Easy NavigationA simple user interface ensures that you find the topics you are looking for.
Excellent SupportOur fast and reliable support answer all your questions to your satisfaction.
Chapter 22.5:Learning OutcomesStudents will learn how to create cumulative frequency graphs!Students will learn how to find information such as mean, min / max values, and the lower and upper quartiles from cumulative frequency graphs!