Frequency Density (Edexcel IGCSE Maths A (Modular))

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Frequency Density

What is frequency density?

  • Frequency density is given by the formula

    • frequency space density equals fraction numerator frequency over denominator class space width end fraction

  • 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 10 over 20 equals 1 half

      • 20 data values spread over a class interval of width 100 would have a frequency density of 20 over 100 equals 1 fifth

      • As 1 half greater than 1 fifth 

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
s m/s

Frequency

20 less or equal than s less than 40

5

40 less or equal than s less than 50

15

50 less or equal than s less than 55

28

55 less or equal than s less than 60

38

60 less or equal than s less than 70

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
s m/s

Frequency

Class width

Frequency density

20 less or equal than s less than 40

5

40 - 20 = 20

5 ÷ 20 = 0.25

40 less or equal than s less than 50

15

50 - 40 = 10

15 ÷ 10 = 1.5

50 less or equal than s less than 55

28

55 - 50 = 5

28 ÷ 5 = 5.6

55 less or equal than s less than 60

38

60 - 55 = 5

38 ÷ 5 = 7.6

60 less or equal than s less than 70

14

70 - 60 = 10

14 ÷ 10 = 1.4

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Roger B

Author: Roger B

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

Dan Finlay

Author: Dan Finlay

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Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.