# Tables, Column and Line Graphs

> Read tables, picture graphs, column graphs and line graphs, read between points, spot a misleading scale and work with temperatures.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/tables-and-graphs/. Updated 4 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The reading challenge
Class 5K is in a reading challenge. Every afternoon, Mr Lee writes on the board how many books the class finished that day. By Friday the board is a mess of numbers.

Hana turns them into a column graph. Now anyone can see at a glance that Thursday was the best day and Wednesday the worst. "A graph shows the story in the numbers," says Mr Lee. "But you still have to read it carefully."

**In short:** A table lists the numbers, and a graph draws them so you can compare at a glance. Always read the title, the labels and the scale first. Column graphs compare groups, and line graphs show how something changes over time, such as the temperature during a day.

## Before you start

- Adding, subtracting and finding an average (see Averages).
- Negative numbers on a number line (see Negative and Positive Numbers).

## Read the labels first

### Key idea: Before you answer any graph question
1. Read the **title**: what is the graph about?
2. Read each **axis label** and its units.
3. Work out the **scale**: how much is each gridline worth?

## Picture graphs

A picture graph uses a symbol for a number of things. The **key** tells you how many one symbol stands for.

If one symbol stands for 4 children, then $5\frac{1}{2}$ symbols stand for $5 \times 4 + 2 = 22$ children.

## Column graphs

*Diagram: Column graph titled Books read by Class 5K. Monday 6, Tuesday 9, Wednesday 4, Thursday 10, Friday 7. The scale goes from 0 to 10 in steps of 2*
*Each gridline is worth 2 books. Tuesday's column stops halfway between 8 and 10, so it shows 9.*

### Worked example: Reading the column graph
- Thursday is the tallest column: 10 books.
- Wednesday is the shortest: 4 books.
- Total for the week: $6 + 9 + 4 + 10 + 7 = 36$ books.
- Average per day: $36 \div 5 = 7.2$ books.

### Watch out: A scale that does not start at 0
If the scale starts at 90 instead of 0, a column for 100 can look twice as tall as a column for 95. The real difference is only 5. Always check where the scale starts.

## Line graphs and temperature

A line graph joins points to show how something changes over **time**. Temperature is measured in degrees Celsius (°C). Water freezes at 0°C and boils at 100°C.

| Time | 6 am | 9 am | 12 noon | 3 pm | 6 pm | 9 pm |
|---|---|---|---|---|---|---|
| Temperature (°C) | 4 | 9 | 15 | 17 | 12 | 7 |

### Worked example: Reading the changes
- The steepest rise is from 9 am to 12 noon: up 6 degrees.
- The highest temperature is 17°C at 3 pm.
- From 3 pm to 9 pm it falls $17 - 7 = 10$ degrees.

### Exam tip: Reading between points
On a line graph you can read between two points. Halfway between 9 am (9°C) and 12 noon (15°C) is 10:30 am, and halfway between 9 and 15 is 12°C.

Temperatures can go below zero. If a night in Canberra is $-3$°C and the next afternoon is 11°C, the temperature rose $3 + 11 = 14$ degrees.

### Challenge: Selective level: graphs and averages
Using the column graph, how many books must the class read on Saturday for the 6-day average to be 8? The total must be $6 \times 8 = 48$. They have 36, so they need 12.

On a column graph the scale goes up in 50s. A column stops halfway between the third and fourth gridlines, which are 150 and 200. It shows 175.

**Mind map**

```text
Tables and graphs
  First read
    Title
    Axis labels
    Scale
  Picture graphs
    Use the key
  Column graphs
    Compare groups
    Check where the scale starts
  Line graphs
    Change over time
    Read between points
  Temperature
    Celsius
    Below zero
```

## Quick summary

- Read the title, axis labels and scale before you answer.
- In a picture graph, multiply the number of symbols by the key.
- Column graphs compare groups. Line graphs show change over time.
- A scale that does not start at 0 can make small differences look big.
- Water freezes at 0°C and boils at 100°C. From $-3$°C to 11°C is a rise of 14 degrees.

## Quiz

Try these questions from the chapter quiz.

1. In the column graph, how many books were read on Thursday?
   - A. 8
   - B. 9
   - C. 10
   - D. 7
   - Answer: C. 10. Thursday's column reaches the top gridline, which is 10.

2. In the column graph, which day had the fewest books?
   - A. Monday
   - B. Wednesday
   - C. Friday
   - D. Tuesday
   - Answer: B. Wednesday. Wednesday's column is the shortest, at 4.

3. At what temperature does water freeze?
   - A. 0°C
   - B. 100°C
   - C. 10°C
   - D. 32°C
   - Answer: A. 0°C. Water freezes at 0 degrees Celsius.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/tables-and-graphs/#quiz