Frequency Density (Edexcel IGCSE Maths)

Spec point — 6.1A

Frequency density

What is frequency density?

• Frequency density is given by the formula

  • $\mathrm{frequency} \mathrm{density}=\frac{\mathrm{frequency}}{\mathrm{class} \mathrm{width}}$

• 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

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
$20\leq s<40$	5
$40\leq s<50$	15
$50\leq s<55$	28
$55\leq s<60$	38
$60\leq s<70$	14

Answer:

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
$20\leq s<40$	5	40 - 20 = 20	5 ÷ 20 = 0.25
$40\leq s<50$	15	50 - 40 = 10	15 ÷ 10 = 1.5
$50\leq s<55$	28	55 - 50 = 5	*28 ÷ 5 = 5.6
$55\leq s<60$	38	60 - 55 = 5	38 ÷ 5 = 7.6
$60\leq s<70$	14	70 - 60 = 10	14 ÷ 10 = 1.4