EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Statistical diagrams 1
Interpreting and representing data · Lesson 1 of 6
Teacher copy - includes the notes for whoever is teaching from it.
Before We Start
Answer each one, then check.
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
Learning Objectives
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.
Types of Data
|
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. |
Frequency Tables
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".
Two-Way Tables
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.
A Two-Way Table
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 |
Completing a Two-Way Table
|
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
Dual or Composite Bar Chart?
|
DUAL BAR CHART |
COMPOSITE 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. |
▸ 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. |
PART TWO
Pie Charts
Showing how a whole is shared out.
Drawing a Pie Chart
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.
Working Out the Angles
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° |
The Pie Chart
|
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. |
Each student is 6° of the circle. |
Reading a Pie Chart
|
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
Key Terms
|
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. |
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. |
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.
Note: With 30 students, each is worth 12° - a good number to measure. If the class size gives awkward angles, round to the nearest degree and check the total.
Can I...?
☐ 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.
Summary
✓ 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. |
Exam Practice: Statistical Diagrams 1
Answer all questions. Show your working. Questions 1 to 3 are non-calculator. · 20 minutes
▸ Question 1 · 1 mark · Non-calculator. Is the number of people in a car discrete data or continuous data?
▸ Question 2 · 3 marks · Non-calculator. 80 students each study one language: French, Spanish or German. 42 of the students are girls. 17 boys study French. 21 students study…
▸ Question 3 · 3 marks · Non-calculator. 40 people were asked which pet they own. 14 own a dog, 11 own a cat, 5 own a fish and 10 own no pet. Work out the angle for each sector of…
▸ Question 4 · 2 marks · Calculator. The pie chart shows how 900 people travel to work. The angle for bus is 80°. How many people travel to work by bus?
Question 1 · 1 mark · Non-calculator
|
“Is the number of people in a car discrete data or continuous data?” |
HOW TO ANSWER IT Command word: Non-calculator. Worth 1 mark, so plan before writing.
Question 1 · mark scheme
1 mark available. Award a mark for each point made.
▸ Discrete. B1
▸ Model answer. Discrete - it is counted, and can only be a whole number.
Question 2 · 3 marks · Non-calculator
|
“80 students each study one language: French, Spanish or German. 42 of the students are girls. 17 boys study French. 21 students study Spanish, and 12 of them are girls. How many boys study German?” |
HOW TO ANSWER IT Command word: Non-calculator. Worth 3 marks, so plan before writing.
Question 2 · mark scheme
3 marks available. Award a mark for each point made.
▸ 38 boys, or a two-way table started with at least two correct values. P1
▸ 9 boys study Spanish. P1
▸ 12. A1
▸ Model answer. Boys: 80 − 42 = 38. Boys studying Spanish: 21 − 12 = 9. Boys studying German: 38 − 17 − 9 = 12.
Question 3 · 3 marks · Non-calculator
|
“40 people were asked which pet they own. 14 own a dog, 11 own a cat, 5 own a fish and 10 own no pet. Work out the angle for each sector of a pie chart.” |
HOW TO ANSWER IT Command word: Non-calculator. Worth 3 marks, so plan before writing.
Question 3 · mark scheme
3 marks available. Award a mark for each point made.
▸ 360 ÷ 40 = 9, or one correct angle. M1
▸ At least two correct angles. A1
▸ All four correct: 126°, 99°, 45°, 90°. A1
▸ Model answer. 360 ÷ 40 = 9° per person. Dog 14 × 9 = 126°, cat 11 × 9 = 99°, fish 5 × 9 = 45°, none 10 × 9 = 90°.
Question 4 · 2 marks · Calculator
|
The pie chart shows how 900 people travel to work. The angle for bus is 80°. How many people travel to work by bus? (2 marks) |
|
Question 4 · mark scheme
2 marks available. Award a mark for each point made.
▸ 80/360 × 900, or 900 ÷ 360 = 2.5. M1
▸ 200. A1
▸ Model answer. 80/360 × 900 = 200 people