Building Scatter Plots from Bivariate Data

Lesson 1 of 2: Scatter Plots

In this lesson:

• See why two columns of data need a new kind of graph
• Build a scatter plot: axes, scale, labels, points

What You Will Be Able To Do

By the end of this lesson, you should be able to:

1. Explain what bivariate data is and why a scatter plot displays it
2. Choose appropriate axes and a scale for a data set
3. Construct a scatter plot by plotting ordered pairs, unconnected

Do Students Who Study More Score Higher?

Can the study-time column alone answer this? Can the score column alone?

Start by Plotting One Student

Student A studied 0.5 hours and scored 62%.

That's the ordered pair — one point.

Plotting a point: a skill you've had since grade 6.

Bivariate Data: Two Measurements, One Individual

• Bivariate = "two variables"
• Each individual contributes two measurements at once
• Example: each student gives us (study time, test score)

Every Point Is a Person

• One point on a scatter plot = one individual
• Its position encodes both measurements at once
• A point is never just an isolated number

Why Not Just Connect the Dots?

• A line graph connects points to show change over time
• A scatter plot leaves points unconnected
• We read the overall cloud, not a path from point to point

Step 1: Choose Axes and a Fitting Scale

• Explanatory variable (study time) goes on the horizontal axis
• Response variable (test score) goes on the vertical axis
• Scale each axis to just span the data: study 0-5, scores 50-100

Why Scale Choice Makes or Breaks the Plot

• Too compressed → all points clump into a blob
• Too loose → the pattern is diluted across empty space
• A fitting scale lets the trend actually show

Step 2: Label Axes and Plot Carefully

Find the x-value, find the y-value, mark where they meet.

Step 3: Leave Them Unconnected

The completed cloud drifts upward — more study, higher scores.

Axis Choice Is a Convention, Not a Cause

• We chose study time for the horizontal axis
• That choice doesn't claim studying causes the score
• The same data plotted either way shows the same relationship

Quick Check: What Do You Notice?

Look back at the completed cloud.

What overall pattern do you see? Is there a point that doesn't fit the rest?

Spot the Error in This Plot

This plot uses a badly compressed vertical scale.

The data really does trend upward. Why can't you see it? How would you fix it?

Your Turn: Build One From Scratch

Data: outdoor temperature vs. ice-cream sales for 12 days.

1. Choose which variable goes on each axis
2. Scale each axis to fit the data
3. Label with units, then plot — unconnected

Key Takeaways From This Lesson

✓ Bivariate data = two measurements per individual
✓ Each point is a person; read the cloud
✓ Scale to fit the data so the pattern shows

Watch out: the x-axis variable is a choice, not the cause
Watch out: a squashed scale hides real patterns

Where We Go From Here Next

You can now build a scatter plot and see the cloud's shape.

Next: how to describe that shape — up or down, straight or curved — and what stray points and clusters mean.