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Mathematical Reasoning · Module 18

Data & Graphs

Read tables, bar charts and pictographs — find totals, differences and averages from data, with four tiers of practice.

Page 1 · Introduction

Reading information from data

Tests often show information as a table, a bar chart, or a pictograph, then ask you a question about it. The skill is reading the values carefully, then doing a small calculation — a total, a difference, or an average.

The big ideaRead the values first, exactly as shown. Then decide what the question wants: add them (total), subtract two (difference), or add and divide (average). Slow reading beats fast guessing.
💡We use simple worded data so you can focus on the method. On the real test the data may be a chart, but the thinking is identical.
On the real testWhere this appearsInterpreting data appears in Mathematical Reasoning (25% of your mark, computer-based, no calculator from 2025). Careful reading of the values is where most marks are won or lost.

Page 2 · Totals & differences

Adding and comparing

The most common questions ask for a total (add everything) or a difference (subtract the smaller from the larger).

A shop sold 12 apples, 9 oranges and 15 pears. How many pieces of fruit in total?
Add them all: 12 + 9 + 15 = 36.
36
Class A has 28 students, Class B has 22. How many more in Class A?
Difference: 28 − 22 = 6.
6

Page 3 · Averages

Finding the average (mean)

The average (mean) = add up all the values, then divide by how many there are.

A student scored 6, 8 and 10 on three quizzes. What is the average?
Add: 6 + 8 + 10 = 24. Divide by 3: 24 ÷ 3 = 8.
8
Four days of rain: 2, 4, 5 and 5 mm. What is the average per day?
Add: 2 + 4 + 5 + 5 = 16. Divide by 4: 16 ÷ 4 = 4 mm.
4 mm

Page 4 · Pictographs

When one symbol means several

In a pictograph each symbol stands for a number. Multiply the symbols by what each one is worth.

In a pictograph, each ★ means 5 books. A shelf shows 6 stars. How many books?
6 stars × 5 books each = 30 books.
30
Each ★ = 10 cars. A row shows 4 and a half stars. How many cars?
4.5 × 10 = 45 cars.
45
Level 1 · Easy

Warm up

Simple totals and differences. Tap to check.

1. A box has 7 red, 8 blue and 5 green balls. How many balls in total?
A 19
B 20
C 21
D 18
7 + 8 + 5 = 20.
2. Team A scored 15 goals, Team B scored 9. How many more did A score?
A 5
B 7
C 6
D 4
15 − 9 = 6.
3. Each ★ means 2 apples. A basket shows 5 stars. How many apples?
A 7
B 12
C 10
D 8
5 × 2 = 10 apples.
Level 2 · Medium

Building up

Averages and larger data.

1. Three tests scored 12, 15 and 18. What is the average?
A 14
B 16
C 15
D 17
12 + 15 + 18 = 45. 45 ÷ 3 = 15.
2. A shop sold 24, 30 and 26 drinks over three days. Total sold?
A 78
B 80
C 82
D 76
24 + 30 + 26 = 80.
3. Each ★ means 10 people. A chart shows 7 stars. How many people?
A 60
B 70
C 80
D 75
7 × 10 = 70 people.
Level 3 · Hard

Getting tougher

Two-step questions from data.

1. Four scores: 8, 10, 14 and 12. What is the average?
A 10
B 11
C 12
D 13
8 + 10 + 14 + 12 = 44. 44 ÷ 4 = 11.
2. A table shows 45 boys and 39 girls. How many more chairs are needed if each child needs one, and there are 70 chairs?
A 12
B 14
C 16
D 10
Total children 45 + 39 = 84. Chairs needed beyond 70: 84 − 70 = 14.
3. Each ★ = 20 books. A shelf shows 3 and a half stars. How many books?
A 60
B 70
C 65
D 80
3.5 × 20 = 70 books.
Level 4 · Challenge

Challenge

Multi-step data reasoning.

1. Five days of sales: 20, 25, 15, 30 and 10. What is the average per day?
A 18
B 20
C 22
D 24
Total 20+25+15+30+10 = 100. 100 ÷ 5 = 20.
2. A pictograph: each ★ = 8 cars. Monday 4 stars, Tuesday 6 stars. How many cars over both days?
A 72
B 80
C 64
D 88
Monday 4×8 = 32, Tuesday 6×8 = 48. Total 32 + 48 = 80.
3. Three classes have 26, 24 and 28 students. If they share equally into 3 new groups, how many per group?
A 24
B 26
C 28
D 27
Total 26 + 24 + 28 = 78. 78 ÷ 3 = 26 per group.

Page 9 · Well done

You’ve finished Data & Graphs

You can now read totals, differences and averages from tables, charts and pictographs. The trick is always the same: read the values carefully first, then do the small calculation the question asks for.

RememberRead the values exactly as shown. Then: add for a total, subtract for a difference, add-and-divide for an average.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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