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Module 5 · L01 of 8 ~30 min MST-12-S2-08 ⚡ +70 XP available

Introduction to Bivariate Data and Scatterplots

Bureau of Meteorology records daily temperature and ice-cream sales across Australian cities, one number predicts the other surprisingly well. In this lesson you will learn what bivariate data is, how to plot it on a scatterplot, and how to read and interpret the pattern of points.

Think first, A researcher records hours of study and exam score for 20 students. What kind of graph would best show the relationship between those two variables?
0/5QUESTS
1

Orient to bivariate data

Connect paired variables, scatterplots and the lesson vocabulary.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Think First, recall from memory
+5 XP warm-up

A researcher records hours of study and exam score for 20 students. What kind of graph would best show the relationship between those two variables? Write your thoughts before reading on.

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02
The big idea, two variables, one graph
+5 XP to read

Bivariate data pairs two measurements on each individual, for example (hours studied, exam score) for each student.

A scatterplot places each pair as a point on a coordinate grid. The independent variable goes on the x-axis; the dependent variable goes on the y-axis.

The pattern of points reveals whether the two variables are related and in what direction.

Each dot = one individual's pair of measurements plotted as (x, y).
Independent on x
The variable you choose or that predicts the other (e.g. hours studied) goes on the horizontal axis.
Dependent on y
The variable that responds (e.g. exam score) goes on the vertical axis.
One point = one case
If a student studied 4 hours and scored 72, that student is the point (4, 72).
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What you will learn
Know

Key facts

  • What bivariate data is
  • The role of each axis on a scatterplot
  • What each plotted point represents
Understand

Concepts

  • Why a scatterplot suits bivariate data
  • How to decide which variable is independent
  • What patterns, outliers and clusters mean
Can do

Skills

  • Plot bivariate data on a labelled scatterplot
  • Read coordinates in context
  • Describe the trend shown by a scatterplot
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Key terms, bivariate data
Bivariate dataData collected on two variables for each individual, e.g. (height, weight) or (temperature, ice-cream sales).
ScatterplotA graph that displays bivariate data as a series of points on a coordinate grid, one point per individual.
Independent variableThe variable on the x-axis; typically the predictor or the variable measured first.
Dependent variableThe variable on the y-axis; the response that may change as the independent variable changes.
Data pointA single plotted point representing one individual's pair of measurements, written as (x, y).
TrendThe overall direction or pattern in the scatter of points, upward, downward, or no clear pattern.
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Construct a scatterplot

Place predictor and response variables correctly and build a readable graph.

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Setting up a scatterplot
MST-12-S2-08 core

Bivariate means "two variables." We record two measurements per individual and explore whether they vary together.

How to set up the axes:

  • Draw a horizontal x-axis and a vertical y-axis.
  • Label each axis with the variable name and units.
  • Choose a scale that fits all data points, it does not need to start at zero if the data is in a narrow range.
  • Put the independent variable on x and the dependent variable on y.

Example: A researcher measures daily temperature (°C) and ice-cream sales (units) for 30 days. Temperature is the independent variable (x-axis) because sales may depend on temperature. Ice-cream sales is the dependent variable (y-axis).

Tip: Ask "which variable could predict the other?" That one is usually the independent variable on x. If you are predicting y from x, put the variable you want to predict on y.

A scatterplot displays bivariate data by plotting each (x, y) pair as a point. The explanatory variable goes on the x-axis; the response variable goes on the y-axis. Each point represents one individual or observation.

Pause, copy the axis assignment rule (explanatory/independent variable on x; response/dependent variable on y) and note that each plotted point represents one individual's pair of measurements into your book.

Quick check: A study records hours of sleep (x) and reaction time in ms (y). Which variable belongs on the y-axis?

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Read scatter patterns

Identify trends, clusters and outliers in a scatterplot.

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Reading a scatterplot, patterns, clusters and outliers
MST-12-S2-08 core

Setting up a scatterplot correctly, explanatory variable on x, response on y, one point per individual, gives you a graph ready to interpret. Now ask three questions about the points: what direction does the pattern run (positive, negative, or none), are there separate clusters of points, and are there any outliers sitting far from the main group?

Once points are plotted, ask three questions:

  1. Direction: Does the pattern go up (positive) or down (negative), or is there no consistent direction?
  2. Strength: Are the points tightly grouped near a line (strong) or widely scattered (weak)?
  3. Unusual features: Are there outliers (points far from the main group) or clusters (separate subgroups)?

Example: A scatterplot of study hours (x) vs exam score (y) shows points rising from lower-left to upper-right. The points are fairly close together. One student studied 10 hours but scored only 30%, an outlier in the bottom-right region.

Hours of study Exam score outlier

When reading a scatterplot, identify the overall pattern (direction, form), any clusters (groups of points), and outliers (points far from the main pattern). Describe what the pattern means in context.

Pause, copy the three scatterplot reading tasks: direction and form of the overall pattern, any clusters (separate groups of points), and any outliers (points far from the main pattern) into your book.

Which does NOT belong? Things you describe when reading a scatterplot:

4

Interpret points in context

Explain individual coordinates and the overall association using the variables.

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Interpreting a scatterplot in context
MST-12-S2-08 core

You can now identify direction, clusters, and outliers visually, but an exam answer that says "positive trend" without naming the variables earns no context marks. Every description must use the actual variable names: "as temperature increases, ice-cream sales tend to increase" rather than "x and y are positively related".

Every point represents a real individual. When describing a scatterplot, always use the variable names and units, not just "x" and "y."

Reading a single point: The point (4, 72) on a study-hours vs score plot means "one student studied 4 hours and scored 72%." On a temperature vs sales plot, (28, 350) means "on a day that reached 28°C, 350 ice-creams were sold."

Describing the overall pattern:

  • State the direction: "As temperature increases, ice-cream sales tend to increase."
  • State the strength: "The points are fairly closely grouped, suggesting a moderately strong relationship."
  • Mention outliers: "One outlier at approximately (12°C, 380 sales) is unexpectedly high for a cool day."
Exam tip: Describing a pattern without naming the variables loses marks. Always say "as [x variable name] increases, [y variable name] tends to..."

Contextual interpretation means describing a scatterplot's pattern in the language of the variables, not just 'positive correlation' but 'as study hours increase, test scores tend to increase'. Always reference the actual variable names.

Pause, copy the contextual description template: "As [x-variable name] increases, [y-variable name] tends to [increase/decrease]", and note that dropping the variable names loses marks in an exam response into your book.

Complete: On a scatterplot of daily temperature (x) vs ice-cream sales (y), the point (32, 480) represents a day when the temperature was degrees and ice-creams were sold.

5

Work scatterplot examples

Follow three worked examples and compare the decisions each one requires.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · PLOT BIVARIATE DATA

Plot the data below on a scatterplot and describe the trend.

Hours studied12345
Score (%)4555627480
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Hours studied = independent variable (x-axis). Score = dependent variable (y-axis).
Study hours predict the score, not the other way around.
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PROBLEM 2 · IDENTIFY INDEPENDENT/DEPENDENT

A scientist measures shoe size and reading speed for 30 adults. Which is independent and which is dependent?

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Neither variable directly causes the other. We are exploring association, not causation.
When no clear causal direction exists, choose based on what you want to predict.
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PROBLEM 3 · INTERPRET A POINT

A scatterplot shows daily rainfall (mm) on x and umbrella sales on y. What does the point (15, 42) represent?

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x = 15 means 15 mm of rain. y = 42 means 42 umbrellas sold.
Read the coordinates directly from the axis labels.
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6

Apply bivariate foundations

Set up, describe and revisit a complete scatterplot analysis.

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Activity, set up and describe a scatterplot

A café records daily maximum temperature (°C) and cups of hot coffee sold over 6 days:

Temp (°C)121518222528
Coffee sold958874605238
  1. Identify the independent and dependent variables. Justify your choice.
  2. Describe the axis labels and scale you would use.
  3. Describe the trend in the data. Would the points go up or down?
  4. What does the point (22, 60) represent in context?
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Revisit your thinking

At the start you were asked what graph would best show the relationship between hours of study and exam score. The answer is a scatterplot it places each student as one point (hours, score), making any pattern immediately visible. A bar chart or line graph cannot show the association between two continuous variables measured for the same individuals.

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7

Answer bivariate questions

Apply scatterplot setup and interpretation in short-answer questions.

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Short answer
ApplyBand 33 marks

Q1. A physiotherapist records sessions attended (x) and pain score out of 10 (y) for 8 patients. (a) Which variable goes on the x-axis? Justify. (b) Describe what the point (6, 2) represents. (c) If the points go from upper-left to lower-right, what does this suggest? (3 marks)

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UnderstandBand 32 marks

Q2. Explain why a scatterplot is more suitable than a bar chart for displaying bivariate data. (2 marks)

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Answers (click to reveal)

Q1 (3 marks):

(a) Sessions attended belongs on the x-axis because it is the independent variable, the number of sessions may predict the change in pain score [1].

(b) The point (6, 2) represents a patient who attended 6 physiotherapy sessions and reported a pain score of 2 out of 10 [1].

(c) The pattern going from upper-left to lower-right (negative trend) suggests that as sessions increase, pain scores tend to decrease, a negative association [1].

Q2 (2 marks): A scatterplot shows both variables simultaneously for each individual as a single point [1], making it possible to see whether there is an association and what direction it takes [1]. A bar chart can only display one variable at a time.

Activity answers: (1) Temperature is independent (x) because it drives coffee demand. (2) x: temperature 10–30°C; y: coffee sold 30–100 units. (3) The points go down (negative trend), as temperature increases, hot coffee sales decrease. (4) The point (22, 60) represents a day when the temperature reached 22°C and 60 cups of coffee were sold.