For IndividualsFor Educators
ExpertMinds LogoExpertMinds
ExpertMinds

Ace your certifications with Practice Exams and AI assistance.

  • Browse Exams
  • For Educators
  • Blog
  • Privacy Policy
  • Terms of Service
  • Cookie Policy
  • Support
  • AWS SAA Exam Prep
  • PMI PMP Exam Prep
  • CPA Exam Prep
  • GCP PCA Exam Prep

© 2026 TinyHive Labs. Company number 16262776.

    PracticeAQA GCSEAQA GCSE Statistics Foundation Tier Paper 2Question 11.3
    Hard4 marksStructured
    Data Visualization and RepresentationFoundationbox plotcumulative frequencyquartiles

    AQA GCSE · Question 11.3 · Data Visualization and Representation

    Height, h (m)Cumulative frequency0102030405060708090100051015202530Height, h (m)051015202530

    The cumulative frequency diagram below shows information about a sample of 100 trees in a large field. The shortest tree in the field is 1 m in height. The tallest tree in the field is 27 m in height. Use this information and the cumulative frequency diagram to complete a box plot for the trees in the field.

    How to approach this question

    A box plot requires 5 values: Minimum, Lower Quartile (LQ), Median, Upper Quartile (UQ), and Maximum. 1. **Minimum and Maximum:** These are given in the question as 1m and 27m. 2. **Median (Q2):** This is the value at the 50% mark. Total frequency is 100, so find 50 on the cumulative frequency axis. Go across to the curve and down to the height axis to read the value. (50 -> 12m). 3. **Lower Quartile (Q1):** This is the value at the 25% mark. Find 25 on the cumulative frequency axis. Go across to the curve and down to the height axis. (25 -> 9m). 4. **Upper Quartile (Q3):** This is the value at the 75% mark. Find 75 on the cumulative frequency axis. Go across to the curve and down to the height axis. (75 -> 16m). 5. **Draw the box plot:** - Draw a vertical line at the minimum (1) and maximum (27). These are the whiskers. - Draw a box from the LQ (9) to the UQ (16). - Draw a vertical line inside the box at the median (12). - Connect the box to the whiskers with horizontal lines.

    Full Answer

    The completed box plot should have: - Minimum value at 1. - Lower Quartile (LQ) at 9. - Median at 12. - Upper Quartile (UQ) at 16. - Maximum value at 27.
    To draw the box plot, we need five key values: 1. **Minimum:** Given as 1 m. 2. **Maximum:** Given as 27 m. 3. **Median (Q2):** The total frequency is 100. The median is at the 50th value. Find 50 on the y-axis of the cumulative frequency diagram, read across to the curve, and then down to the x-axis. This gives a median height of approximately 12 m. 4. **Lower Quartile (Q1):** This is at the (100/4) = 25th value. Find 25 on the y-axis, read across and down. This gives a lower quartile of approximately 9 m. 5. **Upper Quartile (Q3):** This is at the (3*100/4) = 75th value. Find 75 on the y-axis, read across and down. This gives an upper quartile of approximately 16 m. Now we draw the box plot on the provided grid with these five values.

    Common mistakes

    ✗ Reading the values from the cumulative frequency graph inaccurately.\n✗ Mixing up the quartiles and the median.\n✗ Incorrectly constructing the box plot (e.g., box from min to max).
    Question 11.2All questionsQuestion 12.1

    Practice the full AQA GCSE Statistics Foundation Tier Paper 2

    45 questions · hints · full answers · grading

    Sign up freeTake the exam

    More questions from this exam

    Q01A set of data is ordered from smallest to largest. What is the name given to the measure that is ...EasyQ02Look at these sets of data. Which data set has a different range to the others? A: 2, 4, 5, 5, 7,...EasyQ03The probability that a biased coin lands on heads is 2/5. What is the probability that this coin ...EasyQ04Which of these diagrams could be suitable for displaying raw discrete data?EasyQ05.1The table shows the annual sales value (£ million) in the UK of different ways to buy music. Writ...Easy
    View all 45 questions →