Cumulative frequency - Higher
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Statistics
Sets and Venn diagrams
Sampling and bias
Collecting data: types and classes of data
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Frequency tables: finding averages
Grouped frequency tables
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Cumulative frequency - Higher
Histograms and frequency density - Higher
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Standard form calculations
Explainer Video
Summary
Cumulative frequency
In a nutshell
Cumulative frequency graphs show frequency added up as you go along the classes. This means that the frequency for the last class represents the total frequency.
Drawing a cumulative frequency graph
procedure
1. | Add a cumulative frequency column to the frequency table. |
2. | Calculate cumulative frequency by adding frequencies up to and including current row. |
3. | Plot the points at the end of each class. |
4. | Connect the points using a smooth curve or a straight line. |
Example 1
This frequency table shows the height of Mike's classmates. Draw a cumulative frequency graph.
Add a cumulative frequency column and calculate each value.
Height (cm) | Frequency | Cumulative frequency |
| | |
| | |
| | |
| | |
| | |
Plot points at the end of each class (at and ) and connect using a smooth line.
Interpreting cumulative frequency graphs
From cumulative frequency graphs you can read off the lower quartile, median and the upper quartile. Simply work out the position of each and read across to meet the line and down to find out the value.
Example 2
In the example above the LQ, median and UQ are at positions and respectively.
Reading across to the line and down gives that the lower quartile is , the median and the upper quartile .
FAQs - Frequently Asked Questions
How to work out the median from a cumulative frequency graph?
From cumulative frequency graphs you can read off the lower quartile, median and the upper quartile. Simply work out the position of each and read across to meet the line and down to find out the value.
How to draw a cumulative frequency graph?
To draw a cumulative frequency graph: 1. Add a cumulative frequency column to your frequency table. 2. Plot the points at the end of each class. 3. Connect the points using a smooth curve or a straight line.
What is a cumulative frequency graph?
Cumulative frequency graphs show frequency added up as you go along the classes. This means that the frequency for the last class represents the total frequency.
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