top of page

3.3 Representing Data

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: pictograms, bar charts, vertical line charts, dual and composite bar charts. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Draw and read pictograms using a key
  • Draw and read bar charts and vertical line charts
  • Use dual and composite bar charts to compare data
  • Spot charts that are misleading and explain why

Key words

  • Pictogram: A chart that uses symbols to show frequencies. A key tells you what one symbol is worth.
  • Bar chart: A chart with bars of equal width. The height of each bar shows the frequency.
  • Vertical line chart: Like a bar chart but with thin lines instead of bars. Good for discrete numbers.
  • Dual bar chart: Two bars side by side for each category, to compare two sets of data.
  • Composite bar chart: Each bar is split into parts, stacked on top of each other, to show how a total is made up.

Pictograms

Every pictogram needs a key. Part of a symbol stands for part of the key value: half a symbol is half the value, a quarter is a quarter.

Worked example: reading a pictogram

One circle = 8 ice creams, so half = 4 and a quarter = 2.
Wednesday: 3½ circles = 3 × 8 + 4 = 28
Friday: 3¾ circles = 3 × 8 + 6 = 30
Week total: 20 + 12 + 28 + 16 + 30 = 106

Answer: Wednesday 28, Friday 30, total 106 ice creams

Bar charts and vertical line charts

Draw bars of equal width with equal gaps. Label both axes, use an even scale starting at 0, and give the chart a title. For numbers (discrete data), you can draw a vertical line chart with a thin line for each value instead.

Worked example: using a bar chart

(a) How many students are in the class? 9 + 6 + 4 + 3 + 5 = 27
(b) How many more chose football than tennis? 9 − 3 = 6
(c) What fraction chose netball? 6/27 = 2/9

Answer: (a) 27 (b) 6 (c) 2/9

Dual bar charts

A dual bar chart puts two bars side by side for each category so you can compare them. It needs a key to show which bar is which.

Worked example: comparing

On which days were more books borrowed in Week 1 than in Week 2?
Mon 14 < 17, Tue 18 > 15, Wed 11 < 13, Thu 20 < 24, Fri 16 < 19. Only Tuesday.
Totals: Week 1 = 79, Week 2 = 88. Week 2 was busier by 9 books.

Answer: Tuesday only; 9 more books in Week 2

Composite bar charts

In a composite bar chart each part of a bar starts where the last part ended. To find the size of a part, subtract the reading at its bottom from the reading at its top.

Worked example: reading a composite bar

How many Year 11 students travel by bus?
The bus part of the Year 11 bar goes from 30 up to 75.
75 − 30 = 45

Answer: 45 students

Misleading charts

Check the vertical scale. If it does not start at 0, or the steps are uneven, the bars can give a false picture.

Worked example: what is wrong?

Shop B's bar looks three times as tall as Shop A's.
But the sales are 52 and 56: Shop B sold only 4 more, which is less than 8% more.

Answer: the axis does not start at 0, so the difference looks much bigger than it is

Common mistakes

  • Forgetting the key on a pictogram, or reading half a symbol as 1.
  • Drawing bars of different widths, or with no gaps, or with an uneven scale.
  • Reading the top of a composite bar part instead of subtracting to find its size.
  • Not labelling the axes or not giving a key for a dual bar chart.

Revision questions

Try these, then check your answers below each one.

Question 1. In a pictogram, one symbol represents 6 cars. Monday shows 3½ symbols. How many cars does this represent?

Answer: 21

Working: 3 × 6 + 3 = 21 cars.

Question 2. In the same pictogram (one symbol = 6 cars), how many symbols would show 15 cars?

Answer: 2.5

Working: 15 ÷ 6 = 2.5, so two and a half symbols.

Question 3. Which chart is best for comparing two sets of data side by side for each category? (Choose from: Pictogram, Dual bar chart, Composite bar chart, Vertical line chart.)

Answer: Dual bar chart

Working: A dual bar chart puts two bars next to each other for each category.

Related lessons

Continue in the full course

This lesson is section 3.3 (EGCMF0303) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

bottom of page