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Statistical diagrams 1.pptx
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Statistical diagrams 1
Interpreting and representing data
Lesson 1 of 6
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Before We Start
Interpreting and representing data
Lesson 1 of 6
Answer each one, then check.
1
How many degrees are there in a full turn?
2
What is 25% of 360?
3
Write ¼ as a percentage.
4
What is the mode of 3, 5, 5, 7?
5
Work out 360 ÷ 60.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Before We Start - Answers
Interpreting and representing data
Lesson 1 of 6
1
How many degrees are there in a full turn?
360°
2
What is 25% of 360?
90
3
Write ¼ as a percentage.
25%
4
What is the mode of 3, 5, 5, 7?
5 - the most common value.
5
Work out 360 ÷ 60.
6
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Interpreting and representing data
Lesson 1 of 6
1
Tell the difference between types of data.
2
Use frequency tables and two-way tables.
3
Draw and read bar charts, including dual and composite bar charts.
4
Work out the angles for a pie chart and draw it.
5
Read information from a pie chart.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Types of Data
Interpreting and representing data
Lesson 1 of 6
Qualitative (categorical)
Described in words: favourite colour, type of pet.
Quantitative
Numbers: height, number of siblings.
Discrete
Can only take certain values, usually counted: number of goals, shoe size.
Continuous
Can take any value in a range, usually measured: height, time, mass.
Primary data
Collected by you, for example with a questionnaire.
Secondary data
Collected by someone else, for example from a website.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Frequency Tables
Interpreting and representing data
Lesson 1 of 6
A frequency table counts how often each value or category appears.
Tally
Make a mark for each item, grouping them in fives with a line through four: it is easy to count.
Frequency
The total count for each row.
Check the total
The frequencies should add up to the number of items in the data.
Grouped data
When there are many different values, group them into classes such as 10 < t ≤ 20 - "more than 10, up to and including 20".
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Two-Way Tables
Interpreting and representing data
Lesson 1 of 6
A two-way table shows two sets of information about the same group at once.
Rows and columns
One piece of information across the top, the other down the side.
Totals
The last row and column hold totals. Every row and every column adds up to its total.
Filling in gaps
Use the totals: if you know a total and all but one of its parts, subtract.
Reading
Read along a row and down a column to the cell where they meet.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
A Two-Way Table
Interpreting and representing data
Lesson 1 of 6
90 Year 10 students chose one school trip.
Theme park
Zoo
Museum
Total
Boys
23
8
14
45
Girls
17
15
13
45
Total
40
23
27
90
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Completing a Two-Way Table
Interpreting and representing data
Lesson 1 of 6
Using only these facts, find how many boys chose the museum: 90 students; 45 are boys; 40 chose the theme park, 23 of them boys; 15 girls chose the zoo; 23 students chose the zoo in total.
1
Boys who chose the zoo
23 − 15 = 8
2
Boys who chose the museum = boys − theme park − zoo
45 − 23 − 8
3
Work it out
14
ANSWER
14 boys chose the museum
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Dual or Composite Bar Chart?
Interpreting and representing data
Lesson 1 of 6
DUAL BAR CHART
• Two bars side by side for each category.
• One bar for each group, e.g. boys and girls.
• Best for comparing the groups within each category.
• Needs a key.
COMPOSITE BAR CHART
• One bar for each category, split into parts.
• Each part shows one group, stacked on top.
• Best for seeing the total and how it is made up.
• Needs a key.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART TWO
Pie Charts
Showing how a whole is shared out.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Drawing a Pie Chart
Interpreting and representing data
Lesson 1 of 6
The whole circle, 360°, stands for the whole of the data.
Degrees per item
Divide 360 by the total frequency.
Each angle
Multiply each frequency by the degrees per item.
Check
The angles must add up to 360°.
Draw
Draw a radius, measure each angle with a protractor from the last line, and label every sector.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Working Out the Angles
Interpreting and representing data
Lesson 1 of 6
60 students were asked their favourite sport. 360 ÷ 60 = 6, so each student is worth 6°.
Sport
Frequency
Angle
Football
21
21 × 6 = 126°
Tennis
9
9 × 6 = 54°
Swimming
18
18 × 6 = 108°
Other
12
12 × 6 = 72°
Total
60
360°
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
The Pie Chart
Interpreting and representing data
Lesson 1 of 6
Each student is 6° of the circle.
The biggest sector shows the most popular answer at a glance - here, football. A pie chart shows proportions, not numbers: to find how many chose a sport, you need the total as well as the angle.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reading a Pie Chart
Interpreting and representing data
Lesson 1 of 6
A pie chart shows how 720 people travel to work. The sector for "cycle" has an angle of 75°. How many people cycle to work?
1
The sector is a fraction of the whole circle
75/360
2
Multiply by the total
75/360 × 720
3
Simplify: 720 ÷ 360 = 2
75 × 2
ANSWER
150 people
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Interpreting and representing data
Lesson 1 of 6
Frequency
How many times a value or category appears.
Discrete data
Data that can only take particular values, usually counted.
Continuous data
Data that can take any value in a range, usually measured.
Two-way table
A table showing two sets of information about the same group.
Composite bar chart
A bar chart with each bar split into parts for different groups.
Sector
A "slice" of a pie chart.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Interpreting and representing data
Lesson 1 of 6
YOUR TASK
Class Survey
15 minutes
Ask everyone in the class one question with four or five possible answers (for example, "How did you get to school today?"). Record the answers in a two-way table split by boys and girls. Then draw a pie chart of all the answers and a dual bar chart comparing boys and girls.
1
Collect and tally the answers.
2
Fill in the two-way table and its totals.
3
Work out the angles, then draw the pie chart.
4
Draw the dual bar chart.
WHAT A GOOD ANSWER SHOWS
A completed two-way table with correct totals, a pie chart whose angles add to 360°, and a labelled dual bar chart with a key.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Interpreting and representing data
Lesson 1 of 6
Say whether data is qualitative or quantitative.
Say whether data is discrete or continuous.
Complete a frequency table.
Complete and read a two-way table.
Draw and read dual and composite bar charts.
Work out the angles for a pie chart.
Draw a pie chart.
Read information from a pie chart.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Data is qualitative or quantitative; quantitative data is discrete or continuous.
Two-way tables: every row and column adds up to its total.
Pie chart angle = frequency × (360 ÷ total). The angles add to 360°.
Number in a sector = angle/360 × total.
EXAM FOCUS
A pie chart shows how 900 people travel to work. The angle for bus is 80°. How many people travel by bus? (2 marks)
For any pie chart question, first work out what 1° (or 1 person) is worth. Everything else follows from that one number.
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