Scatter Graphs Quizzes
Introduction
Scatter graphs are a powerful way to visualise the relationship between two variables in GCSE Maths. They help students identify patterns, trends, and possible correlations in data. Mastering scatter graphs is essential for understanding real-world data and interpreting exam questions effectively.
Core Concepts
What is a Scatter Graph?
A scatter graph, also called a scatter plot, uses points plotted on a coordinate plane to show the relationship between two variables, usually labelled on the x-axis (independent variable) and y-axis (dependent variable). Each point represents a pair of values from the dataset.
Key Terms
- Independent Variable: The variable you choose or control (plotted on x-axis).
- Dependent Variable: The variable that changes in response (plotted on y-axis).
- Correlation: The relationship between two variables.
- Positive Correlation: As x increases, y tends to increase.
- Negative Correlation: As x increases, y tends to decrease.
- No Correlation: No obvious trend or relationship between x and y.
- Line of Best Fit: A straight or curved line drawn to best represent the trend in the data.
Rules & Steps for Drawing a Scatter Graph
- Identify your two variables and decide which is independent (x-axis) and dependent (y-axis).
- Draw axes with suitable scales for both variables.
- Plot each pair of values as a point on the graph.
- Look for trends: positive, negative, or none.
- Draw a line of best fit (straight or curved) to represent the general trend. The line should balance points above and below it.
- Use the line of best fit to estimate or predict values.
Worked Examples
Example 1: Positive Correlation
Data: Hours studied vs. Exam Score
| Hours Studied (x) | Exam Score (y) |
|---|---|
| 1 | 45 |
| 2 | 50 |
| 3 | 55 |
| 4 | 60 |
| 5 | 65 |
Step 1: Plot points (x, y) on a graph.
Step 2: Draw a line of best fit through the points. Observe the trend: as hours studied increase, exam score increases → positive correlation.
Step 3: Use line of best fit to estimate the score for 3.5 hours:
Draw a vertical line from x = 3.5 to the line of best fit, then a horizontal line to the y-axis. Estimated score ≈ 57.
Example 2: Negative Correlation
Data: Temperature vs. Sales of Hot Chocolate
| Temperature (°C) | Hot Chocolate Sold |
|---|---|
| 5 | 50 |
| 10 | 40 |
| 15 | 30 |
| 20 | 20 |
| 25 | 10 |
Step 1: Plot points.
Step 2: Draw line of best fit. Trend: as temperature increases, sales decrease → negative correlation.
Example 3: No Correlation
Data: Shoe size vs. Maths score
Plot points for different students. Observing the scatter graph, points are spread randomly → no correlation.
Example 4: Using Line of Best Fit for Prediction
Dataset: Hours of sleep vs. Reaction time
After plotting, draw the line of best fit. If someone sleeps 7 hours, draw a vertical line from x = 7 to the line, then horizontal to y-axis to predict reaction time ≈ 0.25 seconds.
Common Mistakes
- Plotting points incorrectly (mixing up x and y axes).
- Using inconsistent scales on axes.
- Drawing line of best fit through every point – line should balance the trend, not touch all points.
- Misinterpreting correlation: correlation does not imply causation.
- Forgetting to label axes with units.
Applications
Scatter graphs are used in exams and real-world contexts:
- Science experiments: measuring effect of temperature on reaction rates.
- Business: analysing sales vs. advertising spend.
- Health: hours of exercise vs. calories burned.
- Education: hours studied vs. exam results.
Strategies & Tips
- Always label axes clearly, including units.
- Choose scales that fit the range of data.
- Observe trends before drawing line of best fit.
- Use the line to make reasonable predictions, but do not extrapolate far beyond the data range.
- Practice identifying positive, negative, or no correlation quickly.
Summary & Encouragement
Scatter graphs provide a visual way to explore relationships between variables. Key points:
- Plot each pair of data points accurately on the graph.
- Look for trends: positive, negative, or none.
- Draw line of best fit to summarise the trend and make predictions.
- Always label axes with variable names and units.
Practice plotting scatter graphs, drawing lines of best fit, and interpreting correlations. This will strengthen your understanding and improve performance in GCSE Maths exams. Attempt the quizzes to reinforce your knowledge!