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D1.3 · Choose and label suitable graphs including scatter plots

Learn to choose and label suitable graphs including scatter plots through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Data

Ontario Grade 8 Mathematics • D1.3

A graph turns data into a picture that is easier to read. The best graph depends on what the data show and what you want readers to notice. In this lesson, you will practise choosing between a bar chart and a scatter plot, then adding labels that make the graph understandable.

What you will learn

Choose a graph that fits the kind of data and the question.
Label a graph so its information is clear.
Read and describe points on a scatter plot.

Start with the data and the question

Data are collected facts or values. Before drawing a graph, ask two questions: What kind of data do I have? What do I want the graph to show?

A bar chart compares amounts in separate groups. For example, it can compare how many students chose each of several activities. Each bar stands for one group, and its height shows that group’s amount.

A scatter plot shows paired values. Each pair belongs together because the two values describe the same item or observation. For example, one point might show the number of minutes someone read and the number of pages they read. A scatter plot helps you see how the paired values are spread out.

The names of groups are categories. A number such as minutes or pages is a numerical value. A bar chart often suits group comparisons. A scatter plot suits pairs of numerical values.

Choose a graph to match the data and the purpose.
Use a bar chart to compare amounts for separate categories.
Use a scatter plot to show paired numerical values.

Make labels do useful work

A graph needs a title that tells what it is about. Each axis also needs a label. An axis is a line along the side or bottom of a graph that helps locate values. Add units when they are known, such as minutes or pages.

On a scatter plot, the bottom axis is the horizontal axis, and the side axis is the vertical axis. State which value belongs on each axis. Keep the same choice throughout the graph. For example, if reading time is on the bottom axis and pages read is on the side axis, every point follows that order.

A scale is the pattern of numbers along an axis. Use equal steps so the spacing between values is consistent. Choose a scale that fits the data and leaves room for the points or bars. Label enough values for a reader to tell where to look.

A bar chart should name the categories and show the amount scale. Bars should be easy to compare. A scatter plot should show both numerical scales and make each paired point clear. If data are hypothetical, say so in the title or caption.

Include a clear title, axis labels, and units when available.
Use equal steps on a numerical scale.
For a scatter plot, state what each axis represents and keep the pair order consistent.

Read a scatter plot carefully

A point on a scatter plot represents one pair of values. Read its bottom-axis value first and its side-axis value second. Together, these tell what the point means.

A group of points may show a pattern. The points may tend to rise, tend to fall, or show no clear direction. Describe only what the graph shows. A pattern in paired data does not, by itself, explain why the values occur.

Do not choose a scatter plot just because the data contain numbers. If the numbers are separate totals for named groups, a bar chart may be clearer. If each observation has two related numerical values, a scatter plot may be suitable.

Each scatter-plot point represents one paired observation.
Read both axis labels before interpreting a point.
Describe visible patterns without claiming they prove a cause.

A quick plan before drawing

First, identify whether the data are group amounts or paired numerical values. Next, choose a graph that suits that structure. Then plan a title, labels, units, and scales. Finally, check that the graph makes the intended comparison or pattern easy to see.

For a bar chart, check that each category has the correct amount. For a scatter plot, check that each point uses the two values from the same observation and that the axes match the stated order.

Check the data type, graph choice, labels, and plotted values.
A well-labelled graph can be understood without guessing.

Worked example

Compare choices by category

A class makes a hypothetical tally of favourite after-school activities: drawing, 6 students; basketball, 9 students; reading, 4 students. Choose a suitable graph and describe its labels.

Hypothetical favourite after-school activities

Each bar shows the number of students in one activity category.

Notice the data structure
Each activity is a separate category, and each has one total. The task is to compare these category amounts.
Choose and label the graph
A bar chart suits this comparison. Give it a title that says the tally is hypothetical. Label the bottom axis “Activity” and the side axis “Number of students.” Use a scale with equal steps that reaches at least 9. Name each bar with its activity.
Check the amounts
The drawing bar should reach 6, the basketball bar 9, and the reading bar 4. With the categories and amount axis labelled, a reader can compare the totals.

Answer: Use a bar chart titled “Hypothetical Favourite After-School Activities.” Label the axes “Activity” and “Number of students.” The bar heights are 6, 9, and 4 for drawing, basketball, and reading.

Check: The categories are separate choices, so a bar chart makes their amounts easy to compare.

Worked example

Plot paired values

The following hypothetical observations pair reading time with pages read: 10 minutes and 5 pages; 20 minutes and 9 pages; 30 minutes and 12 pages; 40 minutes and 17 pages. Choose a graph, label it, and interpret the displayed points.

Hypothetical reading time and pages read

Each point represents one hypothetical paired observation.

Choose the graph
Each observation has two numerical values that belong together: a time and a page count. A scatter plot is suitable because it displays paired values as points.
Set the axes
Put reading time in minutes on the bottom axis and pages read on the side axis. Use equal steps that include all the values. Add a title that identifies the data as hypothetical.
Place and read the points
For each observation, use time first and pages second. The point at 20 minutes and 9 pages means that this hypothetical observation paired those two values. The points generally rise from left to right, so the displayed page counts tend to be higher at larger reading times. This describes the plotted data; it does not establish why the values differ.

Answer: Use a scatter plot titled “Hypothetical Reading Time and Pages Read.” Label the bottom axis “Reading time (minutes)” and the side axis “Pages read.” Plot the four paired observations. The points generally rise from left to right.

Check: The observations are pairs of numerical values, and the plotted points preserve each time-and-pages pairing.

Worked example

Spot a graph that does not fit

A student records the number of library books borrowed by three groups in a hypothetical activity: Group A, 8; Group B, 5; Group C, 11. The student suggests a scatter plot with group names on the bottom axis and book counts on the side axis. Is this a suitable choice? Explain a better choice and labels.

Hypothetical books borrowed by group

Each bar shows a hypothetical count for one group.

Check what each value represents
Each count belongs to a named group. These are category amounts, not two numerical values paired for each observation.
Select a better graph
A bar chart is clearer because it compares the book counts for separate groups. Label the bottom axis “Group” and the side axis “Books borrowed.” Give the chart a title that identifies the counts as hypothetical.
Check the plotted values
The bars should show 8 for Group A, 5 for Group B, and 11 for Group C. This makes the group comparison easy to read without treating group names as numerical values.

Answer: A scatter plot is not the best choice here. Use a bar chart titled “Hypothetical Books Borrowed by Group,” with “Group” on the bottom axis and “Books borrowed” on the side axis. The bar heights are 8, 5, and 11.

Check: The data give one count for each named group, so a bar chart fits the comparison better.

Common mistakes and how to avoid them

Using a scatter plot for any data that contain numbers.

Correction: Use a scatter plot when each observation has two related numerical values. Use a bar chart to compare amounts for named categories.

Leaving out axis labels or units.

Correction: Name what each axis shows and add units when they are known. A reader should not have to guess.

Reversing the values in some scatter-plot pairs.

Correction: Choose what goes on each axis first. Keep that order for every point.

Claiming that a rising pattern proves one value caused another.

Correction: Describe only the pattern visible in the plotted data. A graph alone does not establish a cause.

Lesson summary

Choose a graph that fits the data and the question.
A bar chart compares amounts in separate categories.
A scatter plot shows paired numerical values as points.
Use a clear title, axis labels, units when known, and an even numerical scale.
Read each scatter-plot point using both axis labels, and describe only what the graph shows.

Check your understanding

Question 1

A class records the number of votes for each of four named lunch choices. Which graph is the better fit?

A bar chart, because it compares amounts across categories
A scatter plot, because every amount must be paired with another number
A scatter plot, because the lunch choices are categories
correctIndex

Show answer and explanation

A bar chart, because it compares amounts across categories

Each choice is a category with a vote count, so a bar chart compares the amounts clearly.

Question 2

A scatter plot uses hours of practice on the bottom axis and successful attempts on the side axis. What does one point represent?

A pair of practice hours and successful attempts from one observation
A category name and a bar height
The average of all the plotted values
correctIndex

Show answer and explanation

A pair of practice hours and successful attempts from one observation

Each point represents the two values that belong together for one observation.

Question 3

A scatter plot has clear axis labels and shows points that generally rise from left to right. Which statement is safest?

The plotted points generally rise as the bottom-axis values increase.
The graph proves that the bottom-axis value causes the side-axis value to increase.
The graph is unsuitable because scatter plots cannot show patterns.
correctIndex

Show answer and explanation

The plotted points generally rise as the bottom-axis values increase.

The first statement describes the visible pattern without claiming that one value caused the other.

Key terms

Data: Collected facts or values.
Category: A named group or choice, such as an activity.
Axis: A line on a graph used to show values or categories.
Scale: The pattern of values and equal steps shown along an axis.
Paired values: Two values that belong together for the same observation.
Scatter plot: A graph that shows paired numerical values as points.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation D1.3. It is a study resource, not an official curriculum publication.

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