IGCSE Maths / Working with data

Frequency density revision notes

Edexcel International GCSE Maths (4MA1), chapter 19: Working with data, specification point 6.1a. Free lesson.

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Frequency density is the frequency divided by the class width. It gives the height of a histogram bar, while the bar’s area represents the frequency.

What frequency density measures

The frequency is how many items fall in a class. The frequency density is the height of that class’s bar on a histogram. It is calculated using the class width, so bars with different widths can be compared fairly. Frequency density = frequency ÷ class width. The vertical axis of a histogram measures frequency density, not frequency.

How to find the class width

A class width is the distance from its lower boundary to its upper boundary. Subtract the lower boundary from the upper boundary. Use this width in the frequency density calculation.

How to calculate frequency density

For the class 10 < t ≤ 20, the width is 20 − 10 = 10 minutes. For 20 < t ≤ 40, it is 40 − 20 = 20 minutes. The second class is twice as wide, so its 36 people are spread across more time, giving a lower bar than the first class even though its frequency is higher. For the first class, 26 ÷ 10 = 2.6. For the second class, 36 ÷ 20 = 1.8. The class with frequency 36 has a shorter bar than the class with frequency 26, because its width is greater.

Why a bar’s area gives its frequency

A histogram bar is a rectangle, so its area is its width multiplied by its height. The height is frequency density. Therefore, frequency = frequency density × class width. This explains why bar height alone does not tell you how many items are in a class. For the class with width 20 and density 1.8, the area is 1.8 × 20 = 36. A narrower bar can be taller but still have a smaller area, and therefore a lower frequency.

Avoid using a boundary as the width

For 20 < t ≤ 40, 40 is the upper boundary, not the class width. The width is 40 − 20 = 20. Dividing by 40 would give the wrong density and make the bar too short. Correct calculation: 36 ÷ 20 = 1.8. Incorrect calculation: 36 ÷ 40 = 0.9.