Edexcel 4MA1Cambridge 0580
IGCSE Math Revision Questions by topic Revision notes Past papers Student hub

Cambridge IGCSE Maths (0580) · Topic 9: Statistics · 9.6

Cambridge IGCSE Maths 0580 Cumulative Frequency Questions

Cumulative Frequency 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 cumulative frequency →Cumulative Frequency notes

What the syllabus asks

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

Cumulative Frequency questions: Extended

Extended content, for Papers 2 and 4.

Question 1 Extended non-calculator · easy

The table shows the heights of \(60\) students.
Work out the cumulative frequencies.

Height (h cm)140 < h ≤ 150150 < h ≤ 160160 < h ≤ 170170 < h ≤ 180180 < h ≤ 190
Frequency61422135
Show the worked answer
  1. Add up as you go: \(6\), \(6 + 14 = 20\), \(20 + 22 = 42\), \(42 + 13 = 55\), \(55 + 5 = 60\).

Answer: \(6, 20, 42, 55, 60\)

Question 2 Extended non-calculator · medium

For the heights in the table, write down the points you would plot to draw the cumulative frequency diagram.

Height (h cm)140 < h ≤ 150150 < h ≤ 160160 < h ≤ 170170 < h ≤ 180180 < h ≤ 190
Frequency61422135
Show the worked answer
  1. Plot each cumulative frequency at the upper end of its class, and start at the lower end of the first class with \(0\).

Answer: \((140, 0)\), \((150, 6)\), \((160, 20)\), \((170, 42)\), \((180, 55)\), \((190, 60)\)

Question 3 Extended non-calculator · medium

For the heights in the table, estimate the median height. Assume the heights are spread evenly within each class (a straight line between plotted points).

Height (h cm)140 < h ≤ 150150 < h ≤ 160160 < h ≤ 170170 < h ≤ 180180 < h ≤ 190
Frequency61422135
Show the worked answer
  1. The median is the \(30\)th height. \(20\) are up to \(160\) cm and \(42\) up to \(170\) cm.
  2. \(30\) is \(10\) of the \(22\) students in the \(160\)–\(170\) class: \(160 + \frac{10}{22} \times 10 = 164.5\ldots\) cm.

Answer: \(164.5\) cm

Question 4 Extended non-calculator · medium

For the heights in the table, how many students are taller than \(170\) cm? What percentage of the students are \(160\) cm or shorter?

Height (h cm)140 < h ≤ 150150 < h ≤ 160160 < h ≤ 170170 < h ≤ 180180 < h ≤ 190
Frequency61422135
Show the worked answer
  1. Up to \(170\) cm: \(42\), so taller: \(60 - 42 = 18\).
  2. \(160\) cm or shorter: \(20\) out of \(60\), which is \(33.3\%\).

Answer: \(18\) students; \(33.3\%\)

Question 5 Extended non-calculator · medium

The table shows the times \(80\) people waited at a clinic.
Estimate the median waiting time.

Time (t minutes)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 3030 < t ≤ 40
Frequency12282515
Show the worked answer
  1. Cumulative frequencies: \(12, 40, 65, 80\).
  2. The median is the \(40\)th value, which is exactly at the end of the \(10\)–\(20\) class.

Answer: \(20\) minutes

Question 6 Extended non-calculator · hard

For the heights in the table, estimate the interquartile range. Assume the heights are spread evenly within each class.

Height (h cm)140 < h ≤ 150150 < h ≤ 160160 < h ≤ 170170 < h ≤ 180180 < h ≤ 190
Frequency61422135
Show the worked answer
  1. Lower quartile: the \(15\)th height, \(9\) into the \(150\)–\(160\) class of \(14\): \(150 + \frac{9}{14} \times 10 = 156.42\ldots\)
  2. Upper quartile: the \(45\)th height, \(3\) into the \(170\)–\(180\) class of \(13\): \(170 + \frac{3}{13} \times 10 = 172.30\ldots\)
  3. IQR \(= 172.30\ldots - 156.42\ldots = 15.88\ldots\)

Answer: \(15.9\) cm

Question 7 Extended non-calculator · hard

For the waiting times in the table, estimate the \(90\)th percentile. Assume the times are spread evenly within each class.

Time (t minutes)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 3030 < t ≤ 40
Frequency12282515
Show the worked answer
  1. \(90\%\) of \(80\) is the \(72\)nd value. \(65\) people waited up to \(30\) minutes.
  2. \(72\) is \(7\) into the \(30\)–\(40\) class of \(15\): \(30 + \frac{7}{15} \times 10 = 34.66\ldots\) minutes.

Answer: \(34.7\) minutes

Question 8 Extended non-calculator · hard

For the waiting times in the table, estimate how many people waited more than \(25\) minutes. Assume the times are spread evenly within each class.

Time (t minutes)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 3030 < t ≤ 40
Frequency12282515
Show the worked answer
  1. Up to \(20\) minutes: \(40\). Half of the \(20\)–\(30\) class of \(25\) is \(12.5\), so up to \(25\) minutes: \(52.5\).
  2. More than \(25\) minutes: \(80 - 52.5 = 27.5\), about \(28\) people.

Answer: about \(28\) people (\(27.5\))

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).

Keep going

Questions students ask

Which Cambridge 0580 papers can test cumulative frequency?

Cumulative Frequency is Extended content (syllabus 9.6), 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 cumulative frequency 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