Free GCSE Maths lesson: Statistics

Free LessonsGCSE / Key Stage 4Maths → Tables, Charts and Diagrams

Lesson 64 · GCSE / Key Stage 4 · Maths · Statistics

Tables, Charts and Diagrams

Read, draw and critique common statistical diagrams accurately.

Qualification: GCSEKey Stage 4Subject: MathsStrand: Statistics

GCSE specification fit

Tables, Charts and Diagrams is part of GCSE Maths Statistics.

Read, draw and critique common statistical diagrams accurately. Questions may ask you to complete a table, calculate pie-chart angles, choose a suitable chart or explain why a scale is misleading.

QualificationGCSE Mathematics
Key stageKey Stage 4
StrandStatistics
Tier guidanceFoundation and Higher where specified

What you will learn

  • Read frequency tables.
  • Draw and interpret bar charts, comparative bars and frequency polygons.
  • Use pie charts and line charts.
  • Calculate pie-chart sector angles.
  • Choose suitable diagrams for data.
  • Critique misleading scales and diagrams.

Why this matters

Charts turn data into evidence, but only when scales, labels and categories are handled honestly.

Prior knowledge

You should already be comfortable with:

  • Angles.
  • Percentages.
  • Reading axes.
  • Frequency.

Clear explanation

Main idea

Bar charts compare categories or discrete values. Bars should have equal width and clear gaps for categories. Histograms are different because they show continuous grouped data using frequency density.

Method

Pie charts show parts of a whole. Each sector angle is frequency ÷ total × 360°. Line charts and time-series graphs show change over time, so the horizontal axis should use equal time intervals.

Exam tip

Before interpreting any chart, check the title, axis labels, units, scale and total. A truncated or uneven scale can exaggerate differences.

A frequency polygon is useful for comparing grouped numerical data. Plot each class midpoint against its frequency, then join the plotted points with straight line segments.

Choosing a suitable statistical diagramThree panels show a bar chart for categories, a time-series line graph for change over time, and a frequency polygon using class midpoints for grouped data.Categories: bar chartBusWalkCarfrequencyTime: line graphMonTueWedThuFriequal time intervalsGrouped: frequency polygon5152535plot class midpoints
Checked diagram: each panel uses the chart type that matches the data structure, and the frequency-polygon labels are the class midpoints.

Worked examples

Pie chart angle

12 out of 40 pupils choose bus. Find the sector angle.

Answer: 12 ÷ 40 × 360° = 108°.

Choosing a chart

A teacher records favourite school subjects from a class survey.

Answer: A bar chart is suitable because the data is categorical. A line graph would suggest change over time, which is not the point here.

Frequency polygon point

The class 20 < t ≤ 30 has frequency 14. What point is plotted on a frequency polygon?

Answer: The midpoint is 25, so plot the point (25, 14).

Quick checks

Choose an answer, then check your thinking.

1. Which chart is best for favourite colour categories?

2. What is the pie-chart angle for 15 out of 60 pupils?

Practice questions

Question 1

A class survey records eye colour categories such as brown, blue, green and hazel. Which chart is suitable, and why should the bars have gaps?

Reveal answer and marking guidance

Answer: Bar chart.

Marking: Categories suit bars with gaps and a frequency axis.

Question 2

A club survey shows that 25% of members choose tennis as their favourite sport. Find the pie-chart sector angle for tennis.

Reveal answer and marking guidance

Answer: 90°.

Marking: 25% of 360° = 0.25 × 360° = 90°.

Question 3

A school activity survey has 18 pupils out of 72 choosing football. Find the pie-chart sector angle for football, using the full survey total.

Reveal answer and marking guidance

Answer: 90°.

Marking: 18 ÷ 72 × 360° = 90°.

Question 4

A bar chart comparing test scores uses a vertical axis that starts at 90 instead of 0. Explain why this can be misleading.

Reveal answer and marking guidance

Answer: It can exaggerate differences.

Marking: Small differences can look much larger when the scale is truncated.

Question 5

A travel survey of 120 pupils shows that 36 walk to school. What pie-chart sector angle represents pupils who walk?

Reveal answer and marking guidance

Answer: 108°.

Marking: 36 ÷ 120 × 360° = 108°. Check that the calculation uses the total number of pupils.

Question 6

A line graph shows weekly sales, but the horizontal axis has gaps of 1 week, then 3 weeks, then 1 week drawn equally wide. Explain the problem.

Reveal answer and marking guidance

Answer: The time scale is uneven, so the graph can misrepresent how quickly sales changed.

Marking: Identify the unequal time intervals and explain that equal spacing should represent equal time gaps.

Question 7

A class interval 30 < x ≤ 40 has frequency 9. What point should be plotted on a frequency polygon?

Reveal answer and marking guidance

Answer: (35, 9).

Marking: Use the class midpoint 35 for the horizontal coordinate and the frequency 9 for the vertical coordinate.

Question 8

A survey has 96 pupils. 20 pupils choose art. Find the pie-chart sector angle for art.

Reveal answer and marking guidance

Answer: 75°.

Marking: 20 ÷ 96 × 360° = 75°. Use the whole survey total, not only the pupils in one category.

Question 9

A comparative bar chart uses different vertical scales for two schools placed side by side. Explain why this is misleading.

Reveal answer and marking guidance

Answer: The same bar height represents different frequencies, so the schools cannot be compared fairly. Both charts should use the same vertical scale.

Marking: Identify the inconsistent scales and explain the effect on comparison, then state a fair improvement.

Question 10

A grouped table has intervals 0 < x ≤ 10, 10 < x ≤ 20 and 20 < x ≤ 30 with frequencies 6, 11 and 8. State the three points to plot for a frequency polygon.

Reveal answer and marking guidance

Answer: (5, 6), (15, 11) and (25, 8).

Marking: Use each class midpoint for the horizontal coordinate and the matching frequency for the vertical coordinate.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For tables, charts and diagrams, marks usually come from using the correct total, choosing a suitable representation, labelling axes or sectors and reading scales accurately. Construction questions need ruler accuracy and sensible scales; interpretation questions need a contextual sentence, especially when a graph may be misleading.

Common mistakes

  • Using the wrong chart type: categories usually suit bar charts, while time data often suits line charts.
  • Forgetting the total in pie charts: sector angle is frequency ÷ total × 360°, not frequency × 360°.
  • Reading scales too quickly: check whether each square is worth 1, 2, 5, 10 or another interval.
  • Missing misleading features: truncated axes, uneven intervals and missing labels can change how the data appears.

Extension challenge

Find or sketch a chart with a misleading scale. Explain exactly what makes it misleading and redraw it with a fairer scale.

Reveal answer

Example answer: A misleading bar chart might start the vertical axis at 80 instead of 0, making a small difference look large. A fairer version uses an even scale from 0 and labels both axes clearly.

Exam-board guidance

Tables, Charts and Diagrams appears across GCSE Maths Statistics. All boards expect pupils to read and construct common diagrams, choose suitable representations and comment on scales, totals and misleading presentation.

AQA GCSE Maths

Check labels, units, scales and totals before reading values or drawing a chart. For pie charts, calculate frequency ÷ total × 360° and check the sectors total 360°. For time series, keep equal time intervals on the horizontal axis.

OCR GCSE Maths

Give chart interpretation in context and choose the diagram from the data type: categories, time, grouped continuous data or comparison between groups.

Pearson Edexcel GCSE Maths

Expect multi-step chart questions where you calculate totals, percentages or sector angles before drawing, comparing or criticising the diagram. Mention missing labels, uneven intervals or truncated axes when explaining why a chart is misleading.

Eduqas GCSE Maths

Use a ruler, label axes, choose sensible scales and state what a diagram shows rather than giving a number with no context.

WJEC Wales

Be ready to explain whether a chart is suitable or misleading, especially when axis scales, percentages, missing labels or totals affect the message.

CCEA GCSE Maths

Keep chart construction accurate: equal bar widths, labelled axes, sensible scales, plotted points joined appropriately and clearly calculated pie-chart angles. State the chart type that fits the data.

Next lesson

Next, continue with Scatter Graphs and Correlation.