Frequency Density (Edexcel IGCSE Maths A (Modular))
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
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Frequency Density
What is frequency density?
Frequency density is given by the formula
Frequency density is used with grouped data (i.e. data grouped by class intervals)
It is useful when the class intervals are of unequal width
It provides a measure of how dense data is within its class interval
relative to the width of the interval
For example,
10 data values spread over a class interval of width 20 would have a frequency density of
20 data values spread over a class interval of width 100 would have a frequency density of
As
How do I calculate frequency density?
In questions it is usual to be presented with grouped data in a table
Add two extra columns to the table
one to work out and write down the class width of each interval
the second to then work out the frequency density for each group (row)
Worked Example
The table below shows information regarding the average speeds travelled by trains in a region of the UK.
The data is to be plotted on a histogram.
Work out the frequency density for each class interval.
Average speed | Frequency |
5 | |
15 | |
28 | |
38 | |
14 |
Add two columns to the table
one for class width
one for frequency density
Writing the calculation in each box helps to keep accuracy
Average speed | Frequency | Class width | Frequency density |
5 | 40 - 20 = 20 | 5 ÷ 20 = 0.25 | |
15 | 50 - 40 = 10 | 15 ÷ 10 = 1.5 | |
28 | 55 - 50 = 5 | 28 ÷ 5 = 5.6 | |
38 | 60 - 55 = 5 | 38 ÷ 5 = 7.6 | |
14 | 70 - 60 = 10 | 14 ÷ 10 = 1.4 |
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