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Frequency polygons

Free Printable Frequency polygons PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 2)

Download free frequency polygons worksheets (PDF), GCSE maths past paper questions and worked solutions for Frequency polygons (2P). This is a Grade 2 statistics topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Dr Austin, 1st Class Maths, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our frequency polygons revision notes and worked examples with diagrams, try real GCSE past paper frequency polygons questions with step-by-step solutions, or download a PDF of all frequency polygons worksheet links.

Free Frequency polygons PDF Worksheets & Answers

Grade 2 • Topic 2P
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
Edexcel exam questions & solutions
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
Grade 2 topics
2A - Calculation problems2B - Using a calculator
2C - Systematic listing2D - Fraction of an amount
2E - FDP2F - Simplifying algebra
2G - Writing an expression2H - Function machines
2J - Solving one step equations2K - Angles
2L - Area and perimeter2M - Reading scales
2N - Probability & Probability Scale2P - Frequency polygons
2Q - Unitary method2R - Bar charts
2S - Pie charts2T - Averages
2U - Stem and leaf diagrams
GCSE Maths Grade 2 Revision Notes & Method

Guide to Frequency polygons: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To draw a frequency polygon from a grouped frequency table, first find the midpoint of each class interval by averaging its endpoints: Midpoint = (lower + upper) ÷ 2. Plot each point at (midpoint, frequency).

Join adjacent points in order from left to right using a ruler and straight lines (never a smooth curve). Do NOT join the last point back to the first point, and do not join the ends down to (0, 0).

Example 1: Plot a frequency polygon for this table.

Time (t)fMidPlot
0 < t ≤ 1045(5,4)
10 < t ≤ 20915(15,9)
20 < t ≤ 30625(25,6)
0 4 8 Freq 0 10 20 30 40 Time (t mins)
Plot midpoints (5, 4), (15, 9), (25, 6) and join with straight lines.

Example 2: This frequency polygon for 0–10, 10–20, 20–30, 30–40 has vertices (5, 3), (15, 8), (25, 11), (35, 6). Find total frequency & modal class.

0 4 8 12 Freq 0 10 20 30 40 (25, 11)
• Total: 3 + 8 + 11 + 6 = 28;  Modal class: 20 < t ≤ 30 (peak 11)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Frequency polygons Questions & Answers

Past Paper Example 1 GCSE Jun 2025 3F Q22 / 3H Q1 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The table shows information about the distances that 60 people travel to work.
@@TABULAR0@@
01020304050102030Distance (d miles)Frequency
Draw a frequency polygon for the information in the table.
Worked Solution & Mark Scheme (2 marks)
Plot frequency at each interval midpoint: (5, 12), (15, 25), (25, 10), (35, 8), (45, 5) and connect with straight line segments. M1 A1
01020304050102030Distance (d miles)Frequency
Answer: Points plotted at (5, 12), (15, 25), (25, 10), (35, 8), (45, 5) and joined with line segments
Past Paper Example 2 GCSE Nov 2024 3F Q17 / 3H Q1 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The table shows information about the times, in minutes, 100 people took to complete a
bike race.
Time (t minutes)Frequency120 ⩽ t < 14012140 ⩽ t < 16028160 ⩽ t < 18030180 ⩽ t < 20022200 ⩽ t < 2208
1201401601802002200102030FrequencyTime (t minutes)
On the grid below, draw a frequency polygon for this information.
Worked Solution & Mark Scheme (2 marks)
Plot midpoints (130, 150, 170, 190, 210) against frequencies M1 A1
Answer: Points plotted at (130, 12), (150, 28), (170, 30), (190, 22), (210, 8) and joined with straight lines
Past Paper Example 3 GCSE Nov 2018 3H Q7 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The table gives information about the speeds of 70 cars.
Speed (s mph)Frequency0 < s ⩽ 101410 < s ⩽ 201820 < s ⩽ 302630 < s ⩽ 4012
010203040102030Speed (mph)Frequency
Draw a frequency polygon for this information.
Worked Solution & Mark Scheme (2 marks)
Plot midpoints (5, 14), (15, 18), (25, 26), (35, 12) and join with straight lines. M1 A1
Answer: Points (5, 14), (15, 18), (25, 26), (35, 12) plotted at midpoints and joined with straight line segments

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