Where can I download free cumulative frequency PDF worksheets with answers?

On this MathsLinks page you can download free printable cumulative frequency PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Maths4Everyone, Corbett Practice, Corbett Textbook, plus a printable one-page cumulative frequency revision guide.

What GCSE grade is cumulative frequency (6L)?

Cumulative frequency (topic code 6L) is a Grade 6 statistics topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Cumulative frequency Worksheets (PDF) with Answers — GCSE Maths

Free Cumulative frequency PDF Worksheets & Answers

Grade 6 • Topic 6L

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 6 topics
6A - Recurring decimals	6B - Harder indices
6C - The product rule	6D - Repeated change
6E - Triple brackets	6F - Parallel and perpendicular
6G - Inequalities on graphs	6H - Similar shapes (area and vol)
6J - Negative scale factors	6K - Circle theorems
6L - Cumulative frequency	6M - Box plots
6N - Combined transformations	6P - Capture recapture

Explanation:

Cumulative frequency is a running total of the frequencies. Always plot cumulative frequency points at the upper bound (end value) of each class interval—never the midpoint—and join them with a smooth S-shaped curve.

For a total of N items, read across from N2 (50%) for the Median, from N4 (25%) for the Lower Quartile (LQ), and from 3N4 (75%) for the Upper Quartile (UQ). Then IQR = UQ − LQ.

Example 1: Complete the cumulative frequency table for the times (t mins) of 80 runners.

Solution:

Time (t)	0<t≤20	20<t≤30	30<t≤40	40<t≤60
Freq.	12	28	26	14
Cum. Freq.	12	40	66	80

Plot at upper bounds: (20, 12), (30, 40), (40, 66), (60, 80).

Example 2: From the curve for N = 80, CF = 20 gives 24 mins and CF = 60 gives 37 mins. Find the median and IQR.

Solution:

Median (CF = 40) = 30 mins; LQ = 24, UQ = 37

IQR = 37 − 24 = 13 mins → Answer: Median 30, IQR 13 mins

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Cumulative frequency Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Jun 2023 2H Q9 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The cumulative frequency table gives information about the ages of 80 people working for a company.

(a) On the grid below, draw a cumulative frequency graph for this information. [2 marks]

(b) Use your graph to find an estimate for the median age. [1 mark]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

Plot points (30, 20), (40, 48), (50, 64), (60, 75), (70, 80) at upper bounds M1 A1

Answer (a): Points (30, 20), (40, 48), (50, 64), (60, 75), (70, 80) plotted and joined with a smooth curve or line segments

Part (b) Solution:

reading across from cumulative frequency = 40 gives ~37 years B1

Answer (b): 37 (accept 36 to 38) years

Past Paper Example 2 GCSE Nov 2017 3H Q11 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

The cumulative frequency graph shows information about the weights of 60 potatoes.

(a) Use the graph to find an estimate for the median weight. [1 mark]

(b) Is Jamil correct?
You must give a reason for your answer. [1 mark]

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

Read at CF = 30 → 57 g B1

Answer (a): 57 g

Part (b) Solution:

Grouped data: actual min and max are unknown C1

Answer (b): No (he might not be correct), because the lightest potato could weigh less than 40 g and the heaviest could weigh less than 80 g

Past Paper Example 3 AQA Jun 2025 3H Q13 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

The table shows information about the salary of 90 employees.
@@TABULAR₀@@

(a) Complete the cumulative frequency table.
@@TABULAR₀@@ [1 mark]

(b) Draw a cumulative frequency diagram to represent the data. [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Cumulative frequencies: 66 + 14 = 80, 80 + 5 = 85, 85 + 2 = 87, 87 + 3 = 90 B1

Answer (a): 80, 85, 87, 90

Part (b) Solution:

Plot (20k, 44), (40k, 66), (60k, 80), (80k, 85), (100k, 87), (120k, 90) M1 A1

Answer (b): Points plotted at upper bounds and joined with a smooth curve or straight line segments.

Part (c) Solution:

Reading at s = 32 000 gives approximately 58 employees M1 A1

Answer (c): Answer 58 (accept [55, 60])

← 6K Circle theorems

Back to GCSE questions by topic

6M Box plots →

Cumulative frequency

Free Cumulative frequency PDF Worksheets & Answers

Guide to Cumulative frequency: Explanation, Diagrams & Worked Examples

GCSE Past Paper Cumulative frequency Questions & Answers