Mathematics · Year 9 · Data Interpretation and Probability · Spring Term

Scatter Graphs and Correlation

Students will construct and interpret scatter graphs, identifying types of correlation and drawing lines of best fit.

• National Curriculum Attainment Targets
• KS3: Mathematics - Statistics

About This Topic

Bivariate data involves looking at two variables simultaneously to see if there is a relationship between them. In Year 9, students learn to construct scatter graphs, identify types of correlation (positive, negative, or none), and draw lines of best fit. This is a crucial part of the Statistics attainment targets, teaching students how to interpret data and make evidence-based predictions.

A key lesson in this topic is that 'correlation does not imply causation', just because two things happen together doesn't mean one causes the other. Students also learn the difference between interpolation (predicting within the data range) and extrapolation (predicting outside it). This topic particularly benefits from collaborative investigations where students collect their own data, as it gives them ownership over the variables and a deeper interest in the results.

Key Questions

1. Differentiate between positive, negative, and no correlation on a scatter graph.
2. Analyze whether a strong correlation between two variables always implies causation.
3. Construct a line of best fit and justify its position on a scatter graph.

Learning Objectives

• Construct scatter graphs to represent bivariate data sets.
• Analyze scatter graphs to identify and classify correlation as positive, negative, or none.
• Evaluate the strength of correlation shown on a scatter graph.
• Create a line of best fit on a scatter graph and justify its position.
• Distinguish between correlation and causation using examples.

Before You Start

Plotting Coordinates

Why: Students need to be able to accurately plot points on a Cartesian grid to construct scatter graphs.

Data Representation (Bar Charts, Pictograms)

Why: Familiarity with representing data visually helps students understand the purpose and construction of different graph types, including scatter graphs.

Key Vocabulary

Bivariate Data	Data that consists of two variables, allowing for the investigation of relationships between them.
Scatter Graph	A graph that displays values for two variables for a set of data, with the values shown as a collection of points.
Correlation	The statistical relationship between two variables, indicating whether they tend to move together (positive), in opposite directions (negative), or show no consistent pattern (none).
Line of Best Fit	A straight line drawn on a scatter graph that best represents the trend of the data points, used for prediction.
Causation	The relationship where one event directly causes another event to occur.

Watch Out for These Misconceptions

Common Misconception

Thinking the line of best fit must pass through the origin or connect the first and last points.

What to Teach Instead

The line should have roughly an equal number of points above and below it. Using a clear ruler and 'peer-reviewing' each other's lines helps students understand that the line represents the *trend*, not a path between specific dots.

Common Misconception

Assuming a strong correlation means one variable causes the other.

What to Teach Instead

This is a classic logical error. Use 'spurious correlation' examples to spark discussion. Active learning through debate helps students internalise the idea that data shows a relationship, but logic determines the cause.

Active Learning Ideas

Inquiry Circle: The Human Scatter Graph

Students collect data on themselves (e.g., arm span vs. height). They plot this on a large coordinate grid on the floor or a wall using sticky notes. As a class, they discuss the correlation and use a piece of string to determine the 'line of best fit'.

30 min·Whole Class

Formal Debate: Correlation vs Causation

Present pairs with 'spurious correlations' (e.g., ice cream sales and shark attacks). Students must debate whether one causes the other or if there is a 'hidden variable' (like warm weather) and then present their reasoning to the class.

20 min·Pairs

Think-Pair-Share: The Danger of Extrapolation

Show a scatter graph of a child's growth from age 1 to 10. Ask students to use a line of best fit to predict the person's height at age 50. Pairs discuss why this prediction is likely wrong and the risks of 'predicting the unknown'.

15 min·Pairs

Real-World Connections

• Meteorologists use scatter graphs to analyze the relationship between atmospheric pressure and temperature, helping to predict weather patterns for regions like the UK.
• Market researchers plot customer spending versus advertising expenditure on scatter graphs to understand the impact of campaigns, informing business strategies for companies like Tesco or Sainsbury's.
• Sports analysts examine scatter graphs to see if there is a correlation between training hours and performance metrics for athletes, guiding training programs for teams in the Premier League.

Assessment Ideas

Quick Check

Provide students with three pre-drawn scatter graphs, each showing a different type of correlation (positive, negative, none). Ask students to label each graph with the correct correlation type and write one sentence explaining their choice.

Exit Ticket

Give students a small data set (e.g., hours studied vs. test score). Ask them to construct a scatter graph on a mini-whiteboard. Then, ask them to draw a line of best fit and write one prediction based on their line, stating whether it is interpolation or extrapolation.

Discussion Prompt

Present a scenario: 'Ice cream sales increase when the temperature rises.' Ask students: 'Does this mean hot weather causes people to buy ice cream, or is there another factor at play?' Facilitate a discussion on correlation versus causation, using this or similar examples.

Frequently Asked Questions

How can active learning help students understand scatter graphs?

Active learning makes data personal. When students collect their own data, like measuring their reaction times versus hours of sleep, they are more invested in the outcome. Physically drawing lines of best fit with string on a 'human scatter graph' allows them to experiment with the line's position in real-time. This hands-on approach helps them grasp that the line is an estimate of a trend, making the concepts of correlation and outliers much more intuitive.

What is a 'line of best fit'?

It is a straight line drawn through the center of the data points on a scatter graph. It should follow the general direction of the points and is used to make predictions (estimates) for other values.

What is an outlier?

An outlier is a data point that lies far away from the general trend of the other points. It might be due to a measurement error or a very unusual case, and it is often ignored when drawing a line of best fit.

What is the difference between positive and negative correlation?

Positive correlation means as one variable increases, the other also increases (the line goes up). Negative correlation means as one variable increases, the other decreases (the line goes down).