Can you read information from a range of different graphs? We have seen picture graphs, dot plots, column graphs and bar graphs. Look for keys or scales on a graph to help you understand what information is being presented.

Examples

Example 1

The column graph shows the number of each type of car fixed by the local mechanic.

Which car brand does the mechanic fix most often?

BMW

Mitsubishi

Worked Solution

Create a strategy

Using the graph, identify the car brand with tallest column height.

Apply the idea

The tallest column height with a frequency of 28 is BMW. So the correct answer is option A.

How many Holden or Toyota cars did the mechanic fix in total?

Worked Solution

Create a strategy

Add the column heights of Holden and Toyota.

Apply the idea

The column height of Holdens is 8 and the column height of Toyota is 12.

\displaystyle \text{Total}	\displaystyle =	\displaystyle 8+12	Add column heights
	\displaystyle =	\displaystyle 20	Perform the addition

Idea summary

Check the scale on a column graph. The ticks or marks may not always be worth 1.

Interpret graphs

This video recaps how to answer questions from tables, picture graphs or column graphs, and how these strategies can be used to interpret the data on any kind of graph. Even those that are unfamiliar.

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Examples

Example 2

A marketing company conducted a survey to determine the market share of smartphone manufacturers. They surveyed 4000 people, and the results are given in the table below:

Manufacturer	Responses
\text{Apple}	2051
\text{Samsung}	967
\text{Huawei}	531
\text{Other}	451

Which pie chart most accurately represents this data?

A pie chart showing the data for smartphone market shares. Ask your teacher for more information.

Worked Solution

Create a strategy

Use the data given in the table to find the corresponding sectors.

Apply the idea

Let's start by looking at the market share of Apple. Since 2051 is more than half of 4000, the sector corresponding to Apple should take up more than half the circle. So options A and B are not correct.

If we add the responses of Huawei and Others, we get 531+451=982. which is just a little bit bigger than Samsung. So the Samsung sector should be about equal to the Huawei and Other sectors combined.

So the correct answer is option D.

Idea summary

Pie graphs show the portion that each category takes up out of the whole. The most popular category will have the biggest piece.

Create and interpret line graphs

This video looks at some examples of line graphs with whole number values on the y-axis. It also shows the important features of the graph and how to create one.

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Examples

Example 3

A dachshund puppy is weighed every two weeks.

Week	2	4	6	8
Weight (kg)	1	4	5	5

Construct a line graph of the information given in the table.

Worked Solution

Create a strategy

Plot the points from the table and join them with straight lines.

Apply the idea

\text{Week}

\text{Weight}

The number of weeks will go on the horizontal axis, and the weight will go on the vertical axis since it depends on the number of weeks.

The points from the table are (2, 1),\,(4,4),\,(6,5),\,(8,5). So we can plot these on the graph, then join them with straight lines.

How much weight had the puppy gained from week 2 to week 4?

Worked Solution

Create a strategy

To find the change in weight, subtract the weight in week 2 from the weight in week 4.

Apply the idea

\displaystyle \text{Weight gained}	\displaystyle =	\displaystyle 4-1	Subtract the weights
	\displaystyle =	\displaystyle 3\, \text{kg}

In which weeks did the puppy's weight not change?

From week 4 to week 6.

From week 6 to week 8.

Worked Solution

Create a strategy

Look for the horizontal part in the line graph.

Apply the idea

If the puppy's weight did not change then the line graph will be horizontal. We can see a horizontal line from week 6 to week 8.

So the correct answer is option B.

Idea summary

We can use different kinds of graphs to show data, and some graphs are more suitable than others. In each case, we need to read the heading to see what the graph is showing us, as well as how our graph is labelled.

Outcomes

MA3-18SP

uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables

14.07 Other graphs

Ideas

Are you ready?

Examples

Example 1

Interpret graphs

Examples

Example 2

Create and interpret line graphs

Examples

Example 3

Outcomes

MA3-18SP

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