# Cumulative Frequency Graphs

## Introduction

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.
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### 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.”
## Histograms

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!
Median

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Chapter 22.5: Learning Outcomes
Students 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!

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