IGCSE Math RevisionWorked example 1: Pie chart angle
45 out of 120 students chose football. Find the angle for football in a pie chart.
Solution
- \(\dfrac{45}{120}\times360\).
- \(=135^\circ\).
Answer: 135°
Tip: Each person is worth 360 ÷ 120 = 3°.
Edexcel IGCSE Maths (4MA1) · Unit 6: Statistics & Probability
IGCSE Maths Histograms and Cumulative Frequency Questions and Answers
Histograms and Cumulative Frequency questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
- 4 worked examples
- 3 questions with mark schemes
- Higher tier · calculator allowed
- Free, no sign-in
Practise histograms and cumulative frequency in Unit 6 →Histograms and Cumulative Frequency revision notes
What this topic covers
- Representing Data 1: Choosing frequency tables, two-way tables, bar charts and pie charts for data (4MA1 does not examine stem-and-leaf diagrams, scatter graphs or box plots).
- Representing Data 2: Frequency polygons and histograms.
- Cumulative Frequency 1: Drawing a cumulative frequency curve from grouped data.
- Cumulative Frequency 2: Reading median, quartiles from a c.f. curve.
Histograms and Cumulative Frequency worked examples
Worked example 2: Frequency density
A class \(10<x\le25\) has frequency 36. Find the frequency density.
Solution
- Class width \(=15\).
- \(36\div15=2.4\).
Answer: 2.4
Tip: Histogram bar height is frequency density, not frequency.
Worked example 3: Cumulative frequency table
Frequencies of four classes are 4, 9, 15, 12. Write the cumulative frequencies.
Solution
- Running totals: 4, \(4+9=13\), \(13+15=28\), \(28+12=40\).
Answer: 4, 13, 28, 40
Tip: Plot cumulative frequency at the upper class boundary.
Worked example 4: Quartiles from a list
Find the median and interquartile range of 3, 5, 6, 8, 9, 11, 12, 14, 15, 18, 20.
Solution
- 11 values: median is the 6th value, 11.
- Lower quartile: 3rd value, 6. Upper quartile: 9th value, 15.
- IQR \(=15-6=9\).
Answer: Median 11, IQR 9
Tip: For n values use the (n + 1)/4 and 3(n + 1)/4 positions.
Histograms and Cumulative Frequency exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1
The table gives the times, \( t \) minutes, taken by 50 runners to finish a race. \( 20 \lt t \le 25 \): 3; \( 25 \lt t \le 30 \): 11; \( 30 \lt t \le 35 \): 18; \( 35 \lt t \le 40 \): 12; \( 40 \lt t \le 45 \): 6. Write down the cumulative frequencies for the upper bounds 25, 30, 35, 40 and 45.
Show the answer and mark scheme
- B2 3, 14, 32, 44, 50 (B1 for at least three correct)
Answer: 3, 14, 32, 44, 50
Question 2
The cumulative frequency table gives the heights, \( h \) cm, of 120 students. \( h \le 150 \): 9; \( h \le 155 \): 27; \( h \le 160 \): 58; \( h \le 165 \): 91; \( h \le 170 \): 110; \( h \le 175 \): 120. Which class interval contains the median height?
Show the answer and mark scheme
- M1 median is about the 60th value (120 ÷ 2)
- A1 160 < h ≤ 165
Answer: \( 160 \lt h \le 165 \)
Question 3
The lifetimes, \( t \) hours, of 200 batteries are summarised: \( t \le 10 \): 14; \( t \le 15 \): 52; \( t \le 20 \): 118; \( t \le 25 \): 173; \( t \le 30 \): 200. The cumulative frequency graph is drawn by joining the plotted points with straight lines. Use it to estimate how many batteries lasted more than 22 hours.
Show the answer and mark scheme
- M1 cumulative frequency at 22 hours: 118 + (2/5) × 55 = 140
- M1 200 − their 140
- A1 60 (accept 57 to 63 from a graph)
Answer: 60
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise histograms and cumulative frequency for the exam
- Unit 6 practice: Statistics & Probability in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test histograms and cumulative frequency?
Either Higher tier paper, 1H or 2H, can test histograms and cumulative frequency: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more histograms and cumulative frequency questions?
In the IGCSE student hub: Unit 6 (Statistics & Probability) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.