Scatter Plot Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scatter Plot.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A scatter plot is a graph with one quantitative variable on each axis where each data point is plotted as a dot, revealing relationships between the two variables.

Each dot is one observation — as you scan left to right, the up/down pattern of dots reveals whether the variables tend to increase or decrease together.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A scatter plot shows how two numerical variables move together.

Common stuck point: The procedure for scatter plot is the easy part; the trap is connecting scatter-plot dots automatically. Asking "Does each dot need both an x-value and a y-value?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does each dot need both an x-value and a y-value?

Worked Examples

Example 1

easy

Given the data pairs

(x, y)

(1,2), (2,4), (3,5), (4,4), (5,6)

, describe how to create a scatter plot and identify the direction of the association.

Answer

The scatter plot shows a positive association between

x

and

y

First step

Set up axes: horizontal axis for

x

(explanatory variable), vertical axis for

y

(response variable)

Full solution

2
Plot each ordered pair as a point: $(1,2), (2,4), (3,5), (4,4), (5,6)$
3
Observe the pattern: as $x$ increases, $y$ generally increases
4
Identify association direction: positive association (upward trend from left to right)

Scatter plots reveal the direction (positive/negative/none), form (linear/curved), and strength of association between two quantitative variables. Always label axes and plot one point per data pair.

Example 2

medium

A scatter plot of study hours

(x)

vs. test scores

(y)

shows points clustered tightly around an upward-sloping line. Describe the association in terms of direction, form, and strength. Then identify what an outlier would look like.

Example 3

medium

Pairs

(1,3), (2,5), (3,7), (4,9)

. Do they lie on a line? If so, find the slope.

Example 4

medium

A scatter plot of dose

(x)

vs. effectiveness

(y)

rises sharply, then levels off. Is the relationship linear or non-linear?

Example 5

hard

You have a scatter plot showing a clear curved (parabolic) pattern. Why is a linear correlation coefficient

r

misleading?

Example 6

challenge

A scatter plot shows

5

points:

(1,2), (2,4), (3,5), (4,4), (5,6)

. Compute the mean point

(\bar{x}, \bar{y})

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A scatter plot shows that as temperature increases, ice cream sales also increase. What type of association is this, and what does a scatter plot help us determine that a table of numbers cannot?

Example 2

hard

A scatter plot of age

(x)

vs. reaction time

(y)

shows a curved upward pattern (reaction time increases with age, faster for older individuals). Why would fitting a straight line to this data be problematic?

Example 3

easy

A scatter plot shows hours studied (x) vs test score (y). As hours rise, scores rise. What is the association?

Example 4

easy

On a scatter plot, points go from upper-left to lower-right. Association?

Example 5

easy

Points on a scatter plot are scattered with no clear up/down trend. Association?

Example 6

easy

A scatter plot has points

(1,2),(2,4),(3,6)

. Do they lie on a line?

Example 7

easy

Should you connect the dots on a scatter plot of independent measurements?

Example 8

easy

A scatter plot needs what kind of variables on each axis?

Example 9

easy

One point sits far from a clear linear cluster of dots. What is it called?

Example 10

easy

A scatter plot trend line has slope 3. How much does y rise per unit x?

Example 11

medium

Points

(0,1),(1,3),(2,5),(3,7)

. Find the slope of the line through them.

Example 12

medium

A scatter plot's points fit

y=2x+1

. Predict y when

x=10

Example 13

medium

Data:

(1,5),(2,4),(3,3),(4,2)

. Describe the association and its slope.

Example 14

medium

A scatter plot shows ice-cream sales vs drowning incidents, both rising in summer. Does ice cream cause drownings?

Example 15

medium

Points cluster tightly along a line vs spread loosely around it. Which has stronger correlation?

Example 16

medium

A trend line is

y=-0.5x+10

. At what x does the predicted y reach 0?

Example 17

medium

Two scatter plots have slopes

0.5

and

5

but identical tight clustering. Compare correlation strength.

Example 18

medium

A dataset has points all at

y=5

regardless of x. What is the correlation?

Example 19

medium

A trend line is

y=4x+2

. By how much does y change when x increases by 5?

Example 20

challenge

Points

(1,2),(2,3),(3,5),(4,4),(5,6)

. Estimate the trend-line slope using endpoints.

Example 21

challenge

A trend line

y=3x-2

predicts

y=28

at some x. Find x and judge if extrapolation is risky given data only spans

x\in[0,5]

Example 22

challenge

Adding the point

(10, 50)

to a cluster near the origin sharply tilts the trend line. What is this point's role?

Example 23

easy

A scatter plot of weight

(x)

vs. height

(y)

shows points rising left to right. What is the direction of association?

Example 24

easy

On a scatter plot, the points form a tight cluster around a straight line. Describe the strength of the association.

Example 25

easy

Which type of plot best shows the relationship between two numerical variables?

Example 26

easy

What are the three features we typically describe in a scatter plot?

Example 27

medium

A scatter plot of hours of sleep

(x)

vs. errors on a test

(y)

slopes downward. Describe the association.

Example 28

medium

A scatter plot has many dots and one point far from the rest. What is that point called and what should you check before excluding it?

Example 29

medium

A scatter plot shows the linear pattern

y = 2x + 1

approximately. Predict

y

when

x = 5

Example 30

medium

A scatter plot of points

(1,2), (2,1), (3,2), (4,1), (5,2)

shows what direction?

Example 31

medium

A scatter plot has points all on the horizontal line

y = 4

. Describe the association.

Example 32

hard

A scatter plot trend line goes through

(0, 2)

and

(4, 14)

. Find the slope.

Example 33

hard

Predict

y

x = 10

if the scatter-plot trend line is

y = -0.5x + 8

Example 34

hard

A scatter plot has positive direction, linear form, and a tight cluster. Estimate

r

Example 35

hard

You plot two clusters in a scatter plot, each with its own slope. Is one trend line appropriate?

Example 36

hard

A trend line

y = 0.4x + 2

models test scores from study hours. Interpret the slope in context.

Example 37

hard

A scatter plot has

r = -0.85

. Describe direction and strength.

Example 38

hard

A scatter plot's trend line passes through

(0, 5)

with slope

2

. Write the equation.

Example 39

challenge

A scatter plot shows ice-cream sales rising with temperature. Why is concluding 'heat causes more sales' more justified than 'cars cause accidents' from correlated counts?

Example 40

challenge

You want to plot rainfall vs. crop yield across

30

farms. Why is a scatter plot better than two separate histograms?

← Back to Scatter Plot Practice Mode

Related Concepts

Coordinate Plane Correlation Inference for Regression

Background Knowledge

These ideas may be useful before you work through the harder examples.

coordinate plane