Skip to content
IGCSEMath.com.my
Extended Only Statistics

Histograms for IGCSE Maths

Drawing histograms with unequal class widths using frequency density. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understan

What You Need to Know

Drawing histograms with unequal class widths using frequency density. This subtopic is part of Statistics & Probability in the Cambridge IGCSE Mathematics 0580 syllabus (Extended tier only). Understanding histograms is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Histograms

In IGCSE Extended, histograms display grouped frequency data where the classes may have unequal widths. The y-axis is frequency density (not frequency): frequency density = frequency / class width. The area of each bar represents the frequency. When reading a histogram, multiply frequency density by class width to find frequency. Drawing a histogram requires calculating frequency density for each class.

Step-by-Step Method

  1. 1

    Calculate frequency density

    Frequency density = frequency ÷ class width. Class width = upper boundary − lower boundary.

  2. 2

    Draw the bars

    x-axis: the class intervals. y-axis: frequency density. Bar height = frequency density (not frequency). No gaps between bars.

  3. 3

    Read frequency from a given histogram

    Frequency = frequency density × class width. Read the bar height (FD), multiply by the class width.

  4. 4

    Find total frequency

    Sum all the frequencies (each = FD × class width). Or sum all bar areas.

  5. 5

    Compare class frequencies

    The class with the highest area (not necessarily highest bar) has the highest frequency.

Worked Example

Question

A histogram shows bar for 10≤x<20 with frequency density 4.5, and bar for 20≤x<30 with frequency density 6. Find the frequency in each class and the total for these two classes.

Solution

Class 10≤x<20: width = 10, FD = 4.5. Frequency = 4.5 × 10 = 45 Class 20≤x<30: width = 10, FD = 6. Frequency = 6 × 10 = 60 Total frequency = 45 + 60 = 105 Answers: Frequencies: 45 and 60; Total = 105

Exam Tips for Histograms

  • y-axis is labelled 'frequency density', not 'frequency' — a histogram with frequency on y-axis only works for equal widths.
  • Frequency = FD × width — always multiply, never just read the height as frequency.
  • The tallest bar does NOT necessarily have the highest frequency — check the area (FD × width).
  • No gaps between bars in a histogram — gaps would imply no data in that range.

Practice Questions

Q1: A class 0≤x<5 has frequency 30. Calculate its frequency density.

Show hint

FD = 30/5 = 6.

Q2: Histogram bars: 0≤x<4 (FD=2.5), 4≤x<6 (FD=7), 6≤x<10 (FD=3). Find the frequency of each class.

Show hint

4×2.5=10; 2×7=14; 4×3=12.

Q3: Why can't you directly compare bar heights in a histogram with unequal class widths?

Show hint

Bar height = FD, not frequency. A shorter bar can represent more data if the class width is wider.

Frequently Asked Questions

What is histograms in IGCSE Maths?

Drawing histograms with unequal class widths using frequency density.

Is histograms in the Core or Extended syllabus?

Histograms is part of the Extended only syllabus for IGCSE Mathematics 0580.

How do I revise histograms effectively?

Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on histograms rather than trying to cover everything at once.

Need Help with Histograms?

Book a free trial class and get personalised support from Teacher Rig.

Book Free Trial WhatsApp Us

More on Statistics

Related Subtopics

Explore More

Master Histograms with Expert Help

Book a free 60-minute trial class with Teacher Rig. Get personalised guidance on Statistics and every other IGCSE Maths topic.

Book Free Trial WhatsApp Us