1MA1 · S2StatisticsFoundation & HigherGrades 1–4

Charts & Diagrams

A good chart makes a pattern obvious at a glance; a misleading one hides or exaggerates it. GCSE covers the standard ways of displaying data — bar charts, pie charts, frequency polygons, stem-and-leaf diagrams and time series — and Edexcel asks you both to draw them accurately and to spot when one gives the wrong impression.

40 min Statistics

The big picture

Each chart suits a type of data. Bar charts and pie charts show categories; frequency polygons show the shape of grouped numerical data and make comparisons easy; stem-and-leaf diagrams keep every value while showing the distribution; time series show change over time and reveal trends and seasonal patterns.

Pie charts are about proportions, not totals: two pie charts the same size can represent very different numbers of people. Questions that ask "is this conclusion correct?" often hinge on that.

What you'll learn

Draw and interpret bar charts, including composite and dual bar charts
Draw and interpret pie charts, calculating angles and frequencies
Draw frequency polygons and stem-and-leaf diagrams
Interpret time series and identify misleading representations

Bar charts

Bar charts show frequencies for categories. Bars should be equal widths with gaps between them, and the frequency axis must start at 0.

$\textbf{Dual}$ bar charts put bars for two groups side by side; $\textbf{composite}$ bar charts stack the parts of each total in one bar.

Tip — Label both axes and give the chart a scale with equal steps. Unequal steps are a common way charts mislead.

Pie charts

A pie chart shows each category as a sector. The full circle, $360^{\circ}$ , represents the total.

Angle for a category $= \dfrac{\text{frequency}}{\text{total}} \times 360^{\circ}$ .

To find a frequency from an angle, work out what $1^{\circ}$ represents.

\text{angle} = \dfrac{\text{frequency}}{\text{total}} \times 360^{\circ}

Pie chart angles.

Example 1In a survey of 72 people, 18 chose tea. What angle represents tea?

\dfrac{18}{72} \times 360^{\circ}

Answer

90^{\circ}

Your turnSame method, new numbers — try it before moving on.

In a survey of 60 people, 14 travel by bus. What angle represents bus on a pie chart, in degrees?

Your answer

Show worked solution

Solution

1Each person is $6^\circ$ .
2 $14 \times 6 = 84^\circ$ .

Answer: $84^\circ$

Example 2In a pie chart, a sector of

126^{\circ}

represents 35 people. How many people were surveyed?

1^{\circ}

represents

\tfrac{35}{126}

people.

2Total

= 360 \times \tfrac{35}{126}

Answer100 people

Your turnSame method, new numbers — try it before moving on.

In a pie chart, a sector of $45^\circ$ represents 20 people. How many people were surveyed?

Your answer

Show worked solution

Solution

1 $45^\circ$ is $\frac{1}{8}$ of the circle.
2 $20 \times 8 = 160$ people.

Answer: $160$

Why this works

A larger sector in one pie chart does not mean more people than a smaller sector in a different pie chart. Each chart shows proportions of its own total.

Frequency polygons and stem-and-leaf diagrams

A $\textbf{frequency polygon}$ for grouped data plots each frequency at the $\textbf{midpoint}$ of its class and joins the points with straight lines. Two polygons on one grid make comparison easy.

A $\textbf{stem-and-leaf diagram}$ splits each value into a stem (e.g. tens) and a leaf (units), with leaves in order and a key. It shows the shape of the data while keeping every value, so the median and range can be read directly.

Example 1A stem-and-leaf diagram shows: 2 | 3 5 8; 3 | 1 1 4 6 9; 4 | 0 2 7. Key: 2 | 3 means 23. Find the median and range.

111 values; the median is the 6th value.

2Values in order: 23, 25, 28, 31, 31, 34, ...

3Range

= 47 - 23

AnswerMedian 34, range 24

Your turnSame method, new numbers — try it before moving on.

A stem-and-leaf diagram shows: 1 | 2 4 4 7; 2 | 0 3 5; 3 | 1 6 (key 1 | 2 = 12). Find the median.

Your answer

Show worked solution

Solution

1Nine values: 12, 14, 14, 17, 20, 23, 25, 31, 36.
2The 5th value is $20$ .

Answer: $20$

Tip — Always include a key with a stem-and-leaf diagram. Without it, 2 | 3 could mean 23, 2.3 or 230.

Time series and misleading charts

A $\textbf{time series}$ plots data against time, with points joined by lines. Look for the overall trend (rising, falling, steady) and repeating seasonal patterns.

Charts can mislead through a vertical axis that does not start at zero, unequal scale steps, 3D effects that distort sizes, or missing labels.

Example 1A bar chart of sales has a vertical axis starting at 900. Brand A’s bar reaches 950 and Brand B’s reaches 1000. An advert claims Brand B sells twice as much. Is that correct?

1Bar heights above 900 are 50 and 100, which look like a ratio of 2.

2Actual sales are 950 and 1000.

AnswerNo — B sells only about 5% more. The axis not starting at zero exaggerates the difference.

Think like an examiner

Label axes, sectors and keys.
Show angle or frequency calculations for pie charts.
Explain misleading features specifically.

Charts

\tfrac{f}{\text{total}} \times 360^{\circ}

Pie chart angle.

\text{frequency polygon: plot at midpoints}

Frequency polygons.

Watch out for these

Plotting a frequency polygon at class boundaries.

Plot at midpoints.

Comparing totals between two pie charts by sector size.

Pie charts show proportions; totals may differ.

Leaving out the key on a stem-and-leaf diagram.

Always include a key.

Joining the first and last points of a frequency polygon to the axis without reason.

Join only the plotted midpoints unless told otherwise.

Stretch yourself

School A surveyed 120 students and School B surveyed 300 students about their favourite sport. Football is $105^{\circ}$ on School A’s pie chart and $84^{\circ}$ on School B’s. Sam says more students chose football at School A. Is Sam right?

Hint — Convert each angle back into a number of students.

Reveal solution

SolutionSchool A:

\tfrac{105}{360} \times 120 = 35

students. School B:

\tfrac{84}{360} \times 300 = 70

students. Sam is wrong: School B has twice as many football fans, even though its sector is smaller, because its total is much larger.

\blacksquare

Questions students ask

When should I use a pie chart?

To show how a whole is split into categories, when proportions matter more than exact numbers.

What is a seasonal pattern?

A repeating rise and fall at the same time each year or period, such as higher ice-cream sales every summer.

Why use a frequency polygon rather than a bar chart?

It shows the shape of grouped numerical data and makes it easy to compare two distributions on one diagram.

Key takeaways

Bar charts for categories; start the frequency axis at 0.
Pie chart angle $= \tfrac{f}{\text{total}} \times 360^{\circ}$ ; pie charts show proportions.
Frequency polygons plot at midpoints.
Stem-and-leaf diagrams keep all values and need a key.
Time series show trends; watch for misleading axes and scales.

Exam-style questions

Practise it the way it is examined

3 original questions · 5 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 22 marks

A pie chart shows the choices of 90 people. The sector for pizza is $72^\circ$ . How many people chose pizza?[2]
Show mark scheme
- M1 $360 \div 90 = 4^\circ$ per person
- A1 $18$
Answer: $18$

Question 2Grade 31 mark

A frequency polygon is drawn for grouped data. At what value on the horizontal axis is the class $20 \le t < 30$ plotted?[1]
Show mark scheme
- B1 $25$ (the midpoint)
Answer: $25$

Question 3Grade 42 marks

A bar chart of monthly sales has a vertical axis from 900 to 1000 with no label. Give two reasons it may be misleading.[2]
Show mark scheme
- B1The axis does not start at zero, so differences look larger
- B1The axis is not labelled

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

0 / 0 first-time correct Streak 0Best at this level: 0

Generating a question…

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

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