AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 6

4 marks · Easy difficulty · Multi-step Problem

Use the given bar chart and total of 50 people to find the frequency for Lion and complete the bar chart.

Practise this question

Question

A bar chart titled 'Mascot choices' showing the number of people who chose different mascots out of a total of 50 people. The vertical axis represents the 'Number of people', numbered from 0 to 20 in steps of 2. The horizontal axis lists four mascots: Bear, Rhino, Ox, and Lion. The bar for Bear has a height of 11, Rhino has a height of 20, Ox has a height of 14, and the bar for Lion is missing. Each bar is one grid unit wide with one grid unit between bars. The task asks to complete the bar chart.

Mark scheme

Show the mark scheme Mark scheme for Question 6 awarding up to 4 marks: B1 for reading at least one value correctly (11, 20, or 14); M1 for subtracting the three values from 50 (50 - 11 - 20 - 14) or obtaining 5; A2 for meeting all four drawing criteria: bar drawn to height 5, same width as other bars, all gaps between bars equal, and drawn with straight lines (A1 for meeting two or three of the criteria).

How to answer it

Completing a Bar Chart from a Total Frequency

📋 What this question tests

This question assesses your ability to read scales on a vertical axis, calculate an unknown frequency from a known total, and accurately construct a missing bar following standard statistical chart conventions (consistent bar width, equal spacing, and ruler-drawn edges).

Question 6 (Total: 4 marks)

Completing the "Lion" Mascot Bar

AQA Foundation Mathematics – Statistics & Data Representation

💡 Key Knowledge

  • Reading the scale: On the vertical axis, each large grid square represents 2 units. Half a square represents 1 unit.
  • Total frequency: The sum of all individual categories must equal the overall total of 50 people:
    Bear + Rhino + Ox + Lion = 50
  • Bar chart conventions:
    • Bars must have equal widths (here, 2 grid squares wide).
    • Gaps between bars must be equal (here, 1 grid square wide).
    • Lines should be straight and drawn with a ruler.

📐 Step-by-Step Calculation

  1. Read the existing bar heights:
    • Bear: exactly halfway between 10 and 12 = 11
    • Rhino: line touches 20 = 20
    • Ox: line touches 14 = 14
  2. Sum the known categories:
    11 + 20 + 14 = 45
  3. Subtract from the total (50):
    Lion = 50 - 45 = 5
  4. Identify height on grid:
    A value of 5 is 2.5 grid squares up (halfway between 4 and 6).

✅ What to Draw to Score Full Marks

Draw a vertical bar directly above the label Lion that satisfies all four criteria:

  • Height: Top edge drawn horizontally exactly halfway between 4 and 6 (height = 5).
  • Width: Exactly 2 squares wide (identical to the other three bars).
  • Spacing: Leave a 1-square gap after the Ox bar (consistent with the other gaps).
  • Straight edges: Drawn neatly using a ruler.

Note: Shading is optional—examiners ignore whether the bar is shaded or blank.

🧠 Exam Technique & Examiner Insight

  • Always write down your values: Write the numbers 11 , 20 , and 14 on the chart or in your working space. If you accidentally miscalculate, this guarantees the first method mark ( B1 ).
  • Use a ruler and sharp pencil: Freehand wobbly lines risk losing one of the drawing marks ( A2 drops to A1 ).
  • Check your spacing before drawing: Look at the gap between the y-axis and Bear (1 square), Bear and Rhino (1 square), and Rhino and Ox (1 square). Keep the gap before Lion exactly 1 square!

❌ Common Errors to Avoid

  • Misreading Bear as 10.5 or 12: Each grid square is 2 units, not 1 unit. A bar half a square above 10 is 10 + 1 = 11 , not 10.5 .
  • Drawing the bar attached to Ox: Leaving no gap turns the chart into a histogram. Bar charts for categorical data must have gaps between bars.
  • Incorrect bar width: Making the Lion bar 1 square wide or 3 squares wide instead of matching the other 2-square-wide bars loses an accuracy mark.
  • No working shown when incorrect: The mark scheme states that a bar of incorrect height (e.g. height 3) with no working scores 0 out of 4, whereas showing working could secure method marks.
Mark Scheme Breakdown:
• B1: Correctly reads at least one value ( 11 , 20 , or 14 ). Implied if 5 is seen.
• M1: Correct subtraction method: 50 - 11 - 20 - 14 or answer of 5 (allow one reading slip).
• A2: Fully correct bar drawn meeting all 4 criteria (height 5, correct width, equal gaps, ruled lines).
• (A1 awarded if 2 or 3 of the 4 drawing criteria are met).

Topics

Statistics · Number · 3.6 Statistics · 3.1.1 Structure and calculation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.