Teacher Guide: Scatter Plots

Learn how to make a scatter plot from a table and describe the pattern: form, direction, strength, clusters, gaps and outliers.

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10 questions on Regression. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives

Identify the explanatory and response variables in a data set
Choose suitable axes and equal scales for a scatter plot
Construct a scatter plot from a table and read the coordinates of points
Describe the form, direction and strength of an association
Identify clusters, gaps and outliers and explain what they may mean

Prerequisites

• Plotting ordered pairs on the coordinate plane
• Introduction to Correlation (positive, negative and no correlation)
• Introduction to Regression (what a line of best fit is for)
• Reading data tables and finding the largest and smallest value

Discussion Starters

1. If you plotted your hours of sleep against your mood, which variable would you put on the $x$ -axis, and why?
2. Why do you think we never connect the dots in a scatter plot?
3. Can a pattern be strong and still have an outlier? Can you sketch one?
4. What could explain two clusters in a plot of homework time and quiz scores?

Common Misconceptions

The variable listed first in the table always goes on the $x$ -axis

Remediation: Show a table where the response is listed first (for example score, then hours). Ask which one could influence the other before deciding the axes.

A scatter plot must show a straight line

Remediation: Plot the braking distance data together. Let students see the curve and introduce the word non-linear for patterns that bend.

An outlier is an error and should be erased

Remediation: Discuss the student with 60 minutes of homework and 2 points. Collect real reasons (illness, wrong data entry) and decide together when a point should stay.

Differentiation Ideas

For Struggling Students:

• Provide pre-drawn axes with the scales already marked
• Use small data sets of 4 to 5 points with whole numbers
• Give sentence frames: 'As ___ increases, ___ tends to ___'

For On-Level Students:

• Choose axes and scales for data that does not start near 0
• Describe form, direction and strength for several plots
• Find clusters, gaps and outliers in a real class data set

For Advanced Students:

• Collect their own data on two variables and present the scatter plot
• Compare a linear and a non-linear pattern using the changes in $y$
• Investigate how removing an outlier changes the description

Standards Alignment

8.SP.A.1 (CCSS.MATH.CONTENT.8.SP.A.1)
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association
HSS.ID.B.6 (CCSS.MATH.CONTENT.HSS.ID.B.6)
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related

Lesson Resources

visualTap-to-Plot Grid
Students plot the household size and laundry data point by point and get feedback on each point
activityMeasure Your Class
Pairs measure height and arm span, then the class builds one shared scatter plot on the board
worksheetDescribe the Pattern
Eight scatter plots to describe by form, direction, strength and unusual features

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

A scatter plot is a graph that shows the relationship between two numerical variables measured on the same individuals. Each individual becomes one point

(x, y)

The explanatory variable (the one that may explain or influence the other) goes on the **horizontal $x$ -axis**.
The response variable (the one that responds) goes on the **vertical $y$ -axis**.

To make a scatter plot from a table:

1.Decide which variable is $x$ and which is $y$ .
2.Choose a scale for each axis that covers all the values with equal steps.
3.Label both axes with the variable name and unit.
4.Plot one point for every row of the table. Do not connect the points.

To describe a scatter plot, look at:

Form: do the points follow a straight line (linear) or a curve (non-linear)?
Direction: going up from left to right (positive) or down (negative)?
Strength: are the points close to the pattern (strong), loosely around it (moderate) or widely spread (weak)?
Unusual features: clusters (groups of points), gaps (empty regions) and outliers (points far from the pattern).

Worked Examples

A basketball coach records how many hours seven players practice per week and how many free throws (out of 20) each one makes:

Player	A	B	C	D	E	F	G
Hours	1	2	3	4	5	6	7
Free throws	6	8	9	11	12	14	15

Which variable goes on each axis, and what scales should you use?

Find the explanatory variable

Practice may influence the number of free throws, not the other way round →

x

= hours of practice,

y

= free throws made

Find the range of each variable

Hours: from

1

7

. Free throws: from

6

15

→

x

needs to reach at least

7

y

at least

15

Choose equal steps

x

-axis:

0

8

in steps of

1

y

-axis:

0

20

in steps of

2

(nobody can make more than 20 free throws, and

20 \div 2 = 10

equal steps) → Both axes have equal spacing

Label the axes

x

: Practice per week (hours).

y

: Free throws made (out of 20) → Axes are ready for plotting

Answer: Put **hours of practice on the $x$ -axis (0 to 8, steps of 1) and free throws on the $y$ -axis** (0 to 20, steps of 2), with a label and unit on each axis.

Common Mistakes

Putting the response variable on the $x$ -axis

Why it's wrong: The axes have different jobs. If you plot free throws on the $x$ -axis and practice on the $y$ -axis, the graph suggests that free throws explain practice time.

Correct: Ask: which variable could influence the other? That one is the explanatory variable and goes on the $x$ -axis.

Using uneven steps on an axis (for example 0, 5, 10, 20, 50)

Why it's wrong: Uneven spacing squeezes some points together and stretches others apart, so the pattern you see is false.

Correct: Use the same step all along each axis, for example 0, 10, 20, 30, 40, 50. The two axes may have different steps.

Connecting the points with lines like a line graph

Why it's wrong: The rows of the table are separate individuals, not moments in time. Joining them invents a path that does not exist.

Correct: Leave the points as separate dots. Describe the overall pattern in words (in the next lesson you will draw one line of best fit).

Thinking a steep pattern is a strong pattern

Why it's wrong: Steepness tells you how fast $y$ changes. Strength tells you how closely the points follow the pattern. A pattern with a gentle slope can be very strong, a steep one can be weak.

Correct: Judge strength by how tightly the points hug the line or curve, not by how steep it is.

Why It Matters

Scatter plots are the first thing a scientist, coach or analyst draws when two measurements might be connected:

Sports: A coach plots practice hours against points scored to see if training pays off
Health: Doctors plot age against blood pressure to see how it changes over a lifetime
Weather: Meteorologists plot altitude against temperature (it drops about $6°C$ for every kilometer up)
Business: A shop plots temperature against ice cream sales to plan how much to order
Science: Physicists plot speed against braking distance and discover it is a curve, not a straight line

A scatter plot shows the whole picture at once: the general pattern, the points that break it and the groups hiding in the data. It is the starting point for correlation and for the line of best fit in the next lessons.

Real World Applications

Sports Science: Height and Arm Span

Coaches in swimming and basketball plot height against arm span, because a long arm span is an advantage in both sports.

Example:

For most people the arm span is almost equal to the height, so the points lie close to a straight line going up: a strong, positive, linear pattern.

1Try It Yourself

You want to plot the arm spans of a team. They range from $148$ cm to $182$ cm. Your $y$ -axis starts at $140$ cm and has $10$ grid squares.

What step should each grid square represent (choose from the nice steps 1, 2, 5 or 10)?

Step 1: Write the mathematical expression

Enter the step for one grid square:

Weather: Altitude and Temperature

Mountain guides and pilots know that the air gets colder the higher you go. A scatter plot of altitude against temperature shows how fast.

Example:

Weather balloons measure the temperature every few hundred meters on the way up. Plotted together, the readings fall almost on a straight line going down.

2Try It Yourself

A hiker records the temperature at four altitudes: $(0, 20)$ , $(1, 14)$ , $(2, 7)$ , $(3, 1)$ , with altitude in km and temperature in °C.

How would you describe the scatter plot?

Step 1: Choose the right answer

Choose the best description:

Business: Finding an Outlier

Shops plot the number of social media posts per week against the number of new customers to see if advertising works, and to spot weeks that do not fit.

Example:

A week with many posts but very few customers stands out as an outlier. It often has a reason: a holiday, a website problem or bad weather.

3Try It Yourself

A bakery records five weeks as (posts, new customers): $(2, 30)$ , $(4, 42)$ , $(6, 54)$ , $(8, 66)$ , $(10, 20)$ .

What is the number of posts in the week that is an outlier?

Step 1: Write the mathematical expression

Enter the $x$ -value of the outlier:

Key Takeaways

1A scatter plot shows two numerical variables: each individual is one point $(x, y)$
2The explanatory variable goes on the $x$ -axis, the response variable on the $y$ -axis
3Each axis needs equal steps, a label and a unit; the two axes may use different scales
4Plot one dot per row and never connect the dots
5Describe the pattern by form (linear or non-linear), direction (positive or negative) and strength (strong, moderate, weak)
6Look for unusual features: clusters, gaps and outliers

Frequently Asked Questions

What is the difference between a scatter plot and a line graph?

A line graph follows one quantity over time, so joining the points makes sense. A scatter plot compares two variables for many separate individuals, so the points stay unconnected.

Do both axes have to start at 0?

No. If all heights are between 148 and 182 cm, starting the axis at 140 uses the space better. Just keep equal steps and make the starting value clear on the axis.

What if neither variable explains the other?

Sometimes, like with height and arm span, neither one causes the other. Then you may choose either variable for the

x

-axis. Pick the one you would most likely use to estimate the other.

Should I delete an outlier?

Not automatically. First check whether it is a mistake in the data. If it is a real value, keep it and mention it in your description: outliers often tell the most interesting story.

Glossary

Scatter plot: A graph of points $(x, y)$ that shows the relationship between two numerical variables
Explanatory variable: The variable that may explain or influence the other one; it goes on the $x$ -axis
Response variable: The variable that responds to the explanatory variable; it goes on the $y$ -axis
Form: The shape of the pattern: linear (straight line) or non-linear (curve)
Cluster: A group of points that lie close together, separated from the rest
Outlier: A point that lies far from the overall pattern of the other points

Formula Card

One point per individual

(x, y) = (\text{explanatory}, \text{response})

Every row of the table becomes one point: the first value goes along, the second goes up

Range of a variable

\text{range} = \text{largest} - \text{smallest}

Tells you how much of the axis the values need

Size of one step

\text{step} \geq \frac{\text{largest} - \text{start}}{\text{number of squares}}

Round up to a nice step such as 1, 2, 5 or 10

Teacher Guide: Scatter Plots

Use this lesson with your class

For Teachers

For Struggling Students:

For On-Level Students:

For Advanced Students:

Lesson Content

Definition

Worked Examples

Common Mistakes

Why It Matters

Real World Applications

Sports Science: Height and Arm Span

Weather: Altitude and Temperature

Business: Finding an Outlier

Key Takeaways

Frequently Asked Questions

Glossary

Formula Card

One point per individual

Range of a variable

Size of one step

More in This Topic

Introduction to Regression

Linear Regression

Line of Best Fit

Making Predictions from Data