Where can I download free histograms PDF worksheets with answers?

On this MathsLinks page you can download free printable histograms 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 histograms revision guide.

What GCSE grade is histograms (7R)?

Histograms (topic code 7R) is a Grade 7 statistics topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Histograms Worksheets (PDF) with Answers — GCSE Maths

Free Histograms PDF Worksheets & Answers

Grade 7 • Topic 7R

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
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
1st Class Maths (1) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (2) Edexcel exam questions & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths Takeaway GCSE Maths Takeaway exam questions	Qs	Ans
Maths DIY Exam-style booklet & solutions	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (3) Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	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 7 topics
7A - Surds	7B - Bounds
7C - Proportion (harder)	7D - Algebraic fractions
7E - The quadratic formula	7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs	7H - Rearranging (harder)
7J - Functions (harder)	7K - Iteration
7L - Area of any triangle	7M - The sine rule
7N - The cosine rule	7P - Congruent triangles
7Q - 3D pythagoras / trig.	7R - Histograms
7S - Conditional probability	7T - Exact trig. values (harder)
7U - Area of a segment

Explanation:

In a histogram for grouped continuous data with unequal class intervals, the vertical axis plots Frequency Density rather than frequency, and the area of each bar represents the frequency. Always add a column for class width and use the formula triangle:

Frequency Density = FrequencyClass Width and Frequency = Frequency Density × Class Width. If an interval is cut part-way through (e.g. estimating how many values exceed 25 in a 20 < t ≤ 40 bar), use the fraction of the bar's width.

Example 1: Calculate the frequency densities for the grouped table below.

Mass (m g)	Freq (f)	Width (w)	FD = f ÷ w
0 < m ≤ 10	15	10	1.5
10 < m ≤ 15	20	5	4.0
15 < m ≤ 35	36	20	1.8

Plot bars with heights 1.5, 4.0, and 1.8.

Example 2: Using the table in Example 1, estimate how many items have mass between 12 g and 25 g.

Solution:

Split 12 g to 25 g across both bars:

• 12 to 15 g: 3 × 4.0 = 12

• 15 to 25 g: 10 × 1.8 = 18

Answer: 12 + 18 = 30 items

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Histograms Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE Nov 2017 2H Q17 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

The table gives information about the heights of 150 students.

(a) On the grid, draw a histogram for this information. [3 marks]

(b) Work out an estimate for the fraction of the students who have a height between 150 cm and 170 cm. [2 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

FD = 15÷10 = 1.5, 30÷5 = 6, 51÷5 = 10.2, 36÷5 = 7.2, 18÷15 = 1.2 M2 A1

Answer (a): Histogram with frequency densities 1.5, 6, 10.2, 7.2, 1.2

Part (b) Solution:

30 + 51 + 36 + (5/15 × 18) = 117 + 6 = 123 M1
⇒ 123/150 = 41/50 A1

Answer (b): 123150 (or 4150 or 0.82)

Past Paper Example 2 AQA Nov 2018 3H Q18 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is some information about the ages of people at a concert.
@@TABULAR₀@@

Draw a histogram to represent the information.

Worked Solution & Mark Scheme (3 marks)

Calculate frequency density = FrequencyClass width: M1
• 10 ≤ x < 15: width = 5, FD = 85 = 1.6
• 15 ≤ x < 25: width = 10, FD = 2410 = 2.4 M1
• 25 ≤ x < 40: width = 15, FD = 3015 = 2.0
• 40 ≤ x < 70: width = 30, FD = 3930 = 1.3 A1

Answer: Bars drawn with frequency densities: 1.6, 2.4, 2.0, 1.3

Past Paper Example 3 IGCSE Specimen 1H Q19 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

150 people took part in a survey.
The histogram shows information about the ages of these people.

Work out how many of these 150 people are aged between 50 years and 55 years.

Worked Solution & Mark Scheme (4 marks)

In minor grid units (width × height in small squares): 20–30: 10 × 17 = 170 M1
30–50: 20 × 36 = 720
50–55: 5 × 44 = 220 M1
55–70: 15 × 20 = 300
70–80: 10 × 9 = 90 M1
Total area = 170 + 720 + 220 + 300 + 90 = 1500 small squares
Number of people aged 50–55 = (220 / 1500) × 150 = 22. A1

Answer: 22

← 7Q 3D pythagoras / trig.

Back to GCSE questions by topic

7S Conditional probability →

Histograms

Free Histograms PDF Worksheets & Answers

Guide to Histograms: Explanation, Diagrams & Worked Examples

GCSE Past Paper Histograms Questions & Answers