Bivariate Data and Scatter Plots

Active learning works for bivariate data because students must physically plot points and observe trends to internalize abstract concepts like correlation and outliers. Hands-on data collection and analysis make the abstract relationships between variables concrete and memorable.

• Year 10
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Construct scatter plots from bivariate data sets to visually represent relationships between two numerical variables.
2. Analyze scatter plots to identify and classify the type of correlation (positive, negative, or no correlation).
3. Evaluate the strength of a linear relationship shown on a scatter plot, distinguishing between strong and weak correlations.
4. Identify and describe potential outliers in a scatter plot and explain their possible impact on the observed trend.

Decision Matrix

⏱ 30 min·Pairs

Pairs Data Collection: Height vs Arm Span

Students measure each other's height and arm span in centimetres, record pairs in a table, then plot on a class-shared scatter plot template. They draw a line of best fit by consensus and classify the correlation. Extend by predicting values for new data points.

Prepare & details

Explain how a scatter plot visually represents the relationship between two variables.

Facilitation Tip: During Pairs Data Collection, walk around with a stopwatch to ensure both partners take measurements carefully to avoid inconsistent data collection.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 45 min·Small Groups

Small Groups: Dataset Analysis Relay

Provide three printed datasets on cards (e.g., hours slept vs reaction time). Groups plot one each on mini whiteboards, describe trend and strength, then rotate to critique and replot peers' work. Conclude with whole-class share of findings.

Prepare & details

Differentiate between positive, negative, and no correlation.

Facilitation Tip: In the Dataset Analysis Relay, provide each group with a different colored pen so you can track which plots they have interpreted and where they got stuck.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 25 min·Whole Class

Whole Class: Outlier Investigation

Display a large scatter plot of class-chosen data like steps walked vs phone usage. Students vote on potential outliers via hand signals, justify choices in pairs, then vote to include or exclude and observe trend shifts.

Prepare & details

Construct a scatter plot from a given data set and describe its general trend.

Facilitation Tip: For Outlier Investigation, prepare a large poster of the scatter plot so students can physically circle and move points to see how the trend line shifts.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 20 min·Individual

Individual: Personal Trend Tracker

Students select two variables from their week (e.g., caffeine intake vs alertness score), collect five data pairs, plot individually, and write a one-sentence trend description. Share digitally for class pattern comparison.

Prepare & details

Explain how a scatter plot visually represents the relationship between two variables.

Facilitation Tip: During Personal Trend Tracker, remind students to label axes with units and include a title that clearly states what the variables represent.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Teaching This Topic

Teach scatter plots by having students experience the data first. Ask them to predict relationships before plotting, then let the data challenge their predictions. Use real datasets to show that not all relationships are linear, so students learn to look beyond r-squared values. Avoid rushing to the correlation coefficient; let students describe trends in their own words first.

What to Expect

Students will confidently plot points, describe correlation strength, identify outliers, and explain why correlation does not imply causation. Their explanations will use precise terms like positive/negative/none and include reasoning about hidden variables.

Watch Out for These Misconceptions

Common Misconception

During Pairs Data Collection, watch for students who assume arm span directly causes height or vice versa.

What to Teach Instead

After pairs collect their data, have them share their plots with another pair and discuss whether one variable must cause the other. Prompt them to brainstorm third factors like genetics or nutrition that might influence both.

Common Misconception

During Dataset Analysis Relay, watch for groups that dismiss curved or clustered patterns as 'no correlation'.

What to Teach Instead

Hand each group a sheet with a non-linear example like height vs weight in teens and ask them to sketch a line of best fit. Discuss why the line isn’t perfect but still describes a trend.

Common Misconception

During Outlier Investigation, watch for students who think removing an outlier automatically improves the pattern.

What to Teach Instead

Ask groups to replot the data without the outlier, then compare their new trend line to the original. Discuss whether the relationship strengthens or weakens and why outliers can sometimes mask important trends.

Assessment Ideas

Exit Ticket

After Personal Trend Tracker, collect students’ scatter plots and one-sentence descriptions of the correlation. Check for correct axis labels, units, and accurate use of terms like positive, negative, or none.

Quick Check

During Dataset Analysis Relay, circulate and listen to groups explain their scatter plot’s correlation type. Ask one student from each group to share their group’s conclusion with the class.

Discussion Prompt

After Outlier Investigation, display a plot with an obvious outlier and ask: 'What might explain this point? How would the trend change if we removed it?' Listen for reasoning about causation vs correlation.

Extensions & Scaffolding

• Challenge early finishers to create a residual plot from their Personal Trend Tracker data and calculate the sum of squared residuals to quantify fit.
• For students who struggle, provide pre-printed axes with labeled scales to reduce plotting errors and focus on pattern recognition.
• Deeper exploration: Ask groups to research a real-world dataset, plot it, and present the relationship they found, including any outliers and possible confounding variables.

Key Vocabulary

Bivariate Data	A set of data containing two variables for each individual or event, used to investigate relationships.
Scatter Plot	A graph that displays the relationship between two numerical variables by plotting individual data points as dots on a coordinate plane.
Correlation	A statistical measure that describes the extent to which two variables change together. It can be positive, negative, or absent.
Positive Correlation	A relationship where as one variable increases, the other variable also tends to increase. Points on a scatter plot generally rise from left to right.
Negative Correlation	A relationship where as one variable increases, the other variable tends to decrease. Points on a scatter plot generally fall from left to right.
Outlier	A data point that is significantly different from other data points in the set, potentially affecting the overall trend.