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Cambridge IGCSE Maths (0580) · Topic 9: Statistics · 9.7

Cambridge IGCSE Maths 0580 Histograms Questions

Histograms questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise histograms →Histograms notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Histograms questions: Extended

Extended content, for Papers 2 and 4.

Question 1 Extended non-calculator · easy

The table shows the masses of some parcels.
Work out the frequency density for each class.

Mass (m kg)0 < m ≤ 1010 < m ≤ 1515 < m ≤ 2020 < m ≤ 40
Frequency15203024
Show the worked answer
  1. Frequency density \(= \frac{\text{frequency}}{\text{class width}}\).
  2. \(15 \div 10 = 1.5\), \(20 \div 5 = 4\), \(30 \div 5 = 6\), \(24 \div 20 = 1.2\)

Answer: \(1.5, 4, 6, 1.2\)

Question 2 Extended non-calculator · medium

For the parcels in the table, which class has the tallest bar on a histogram? Explain why it is not the class with the greatest width.

Mass (m kg)0 < m ≤ 1010 < m ≤ 1515 < m ≤ 2020 < m ≤ 40
Frequency15203024
Show the worked answer
  1. The tallest bar has the greatest frequency density: \(15 \lt m \le 20\) with \(6\).
  2. Bar height is frequency density, not frequency: the \(20\)–\(40\) class is wide, so its \(24\) parcels give a low bar of \(1.2\).

Answer: \(15 \lt m \le 20\) (frequency density \(6\))

Question 3 Extended non-calculator · medium

A histogram bar for the class \(20 \lt x \le 30\) has a frequency density of \(2.4\).
Find the frequency of the class.

Show the worked answer
  1. Frequency \(=\) frequency density \(\times\) class width \(= 2.4 \times 10 = 24\).

Answer: \(24\)

Question 4 Extended non-calculator · medium

The table gives the frequency densities from a histogram of some lengths.
Find the frequency of each class and the total frequency.

Length (x cm)0 < x ≤ 2020 < x ≤ 3030 < x ≤ 3535 < x ≤ 50
Frequency density0.52.23.61.0
Show the worked answer
  1. \(0.5 \times 20 = 10\), \(2.2 \times 10 = 22\), \(3.6 \times 5 = 18\), \(1.0 \times 15 = 15\)
  2. Total \(= 10 + 22 + 18 + 15 = 65\)

Answer: \(10, 22, 18, 15\); total \(65\)

Question 5 Extended non-calculator · medium

A class \(40 \lt m \le 60\) has a frequency of \(9\).
Work out the height of its bar on a histogram (its frequency density).

Show the worked answer
  1. Class width \(= 20\).
  2. \(9 \div 20 = 0.45\)

Answer: \(0.45\)

Question 6 Extended non-calculator · hard

Using the frequency densities in the table, estimate how many lengths are between \(25\) cm and \(40\) cm.

Length (x cm)0 < x ≤ 2020 < x ≤ 3030 < x ≤ 3535 < x ≤ 50
Frequency density0.52.23.61.0
Show the worked answer
  1. \(25\) to \(30\): \(2.2 \times 5 = 11\).
  2. \(30\) to \(35\): \(3.6 \times 5 = 18\).
  3. \(35\) to \(40\): \(1.0 \times 5 = 5\).
  4. Total \(= 11 + 18 + 5 = 34\)

Answer: \(34\)

Question 7 Extended non-calculator · hard

On a histogram, the class \(0 \lt x \le 5\) has frequency \(20\) and a bar of height \(4\). The bar for \(5 \lt x \le 15\) has height \(3\).
Find the frequency of the class \(5 \lt x \le 15\).

Show the worked answer
  1. Check the scale: \(20 \div 5 = 4\), so the heights are frequency densities.
  2. Frequency \(= 3 \times 10 = 30\).

Answer: \(30\)

Question 8 Extended calculator · hard

A histogram has three bars: \(0 \lt x \le 10\) with frequency density \(1.2\), \(10 \lt x \le 20\) with \(2.5\) and \(20 \lt x \le 40\) with \(0.9\).
Estimate the mean, correct to 3 significant figures.

Show the worked answer
  1. Frequencies: \(12\), \(25\), \(18\); total \(55\).
  2. Midpoints \(5\), \(15\), \(30\): \(5 \times 12 + 15 \times 25 + 30 \times 18 = 60 + 375 + 540 = 975\).
  3. Estimated mean \(= 975 \div 55 = 17.72\ldots\)

Answer: \(17.7\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test histograms?

Histograms is Extended content (syllabus 9.7), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more histograms questions?

In the 0580 practice for topic 9 (Statistics), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More statistics questions