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# Scatterplots | Lesson

## What's a scatterplot?

A scatterplot displays data about two variables as a set of points in the $xy$-plane.
A scatterplot is a key tool to determine if there is a relationship between the values of two variables.

### What skills are tested?

• Matching the description of a relationship between variables to a scatterplot
• Describing the relationship between variables shown on a scatterplot
• Drawing conclusions from a scatterplot

## What does correlation mean?

Correlation describes how one variable changes as the other changes in a scatterplot.
: As $x$ increases, $y$ tends to increase.
: As $x$ increases, $y$ tends to decrease.
: As $x$ increases, $y$ stays about the same or has no clear pattern.

## What is a linear relationship?

Linearity describes whether or not the trend of the dots in a scatterplot can be approximated by a line.
In a
, data points tend to fall along a line. The scatterplot below shows a linear relationship with a
illustrating how the data might be approximated.
In a
, data points do not fall along a line. The scatterplot below shows a nonlinear relationship with a curve illustrating how the data might be approximated.

## What conclusions can we make based on a scatterplot ?

In context, the meaning of the points in a scatterplot corresponds to the variables represented by each axis.
For example, a teacher collected data on the shoe size and quiz score for every student in her class. In her scatterplot below, the horizontal axis is Shoe Size and the vertical axis is Quiz Score. Each of the $23$ dots represents the shoe size and quiz score of one particular student.

TRY: MATCHING A SCATTERPLOT TO A DESCRIPTION
Which of the following scatterplots suggests a positive linear correlation between $x$ and $y$ ?

TRY: DESCRIBING THE RELATIONSHIP SHOWN IN A SCATTERPLOT
Which of the following best describes the relationship shown in the scatterplot above?

TRY: DESCRIBING THE RELATIONSHIP SHOWN IN A SCATTERPLOT
An engineer created the scatterplot above from data she collected on the speed a car traveled (in kilometers per hour) and how much fuel it used (in liters per $100$ kilometers). What is the best description of this relationship?

TRY: DRAWING CONCLUSIONS FROM A SCATTERPLOT
The scatterplot above shows data Sean gathered about the height and petal length (in centimeters) of all the flowers in the school garden. Based on the scatterplot, which of the following statements are true?

## Things to remember

A scatterplot:
• displays data about two variables as a set of points in the $xy$-plane
• is a key tool to determine if there is a relationship between two variables.
The relationship between variables is described in terms of
and
:
• Do the variables exhibit a positive, negative, or no correlation?
• Is the relationship linear or nonlinear?
Only correlation between variables—not the cause of the relationship—can be determined from a scatterplot.
• Making conclusions about causation requires a well-designed experiment.