Creating Scatter Diagrams
A scatter diagram is a graph used to display the relationship between two variables. Each point on the diagram represents one observation, plotted according to its values for the two variables.
To create a scatter diagram, first label the horizontal (x) and vertical (y) axes with the variables being compared. Then, plot each pair of values as a point on the graph.
Points should be clearly marked to avoid confusion. Using small crosses (×) is a common and effective method because they are distinct and easy to see, especially when points are close together. Avoid using large dots or marks that can overlap and obscure data patterns.
- Label axes with variable names and units.
- Plot each data pair as a point using a small cross (×).
- Ensure points are distinct and clearly visible.
Understanding Correlation
Correlation describes the direction and strength of the relationship between two variables shown on a scatter diagram.
Positive correlation means that as the value of one variable increases, the value of the other variable also tends to increase. The points slope upwards from left to right.
Negative correlation means that as one variable increases, the other tends to decrease. The points slope downwards from left to right, showing an inverse relationship between the variables. Zero correlation means there is no apparent relationship between the variables; the points are scattered randomly with no clear pattern or trend.
- Positive correlation: variables increase together.
- Negative correlation: one variable increases, the other decreases.
- Zero correlation: no clear relationship between variables.
Drawing the Line of Best Fit
A line of best fit is a straight line drawn through the scatter diagram to represent the general trend of the data.
This line is drawn by eye (observation), not by calculation, and should extend across the entire range of data points on the graph.
The line does not have to pass through any of the points exactly. Instead, it should be positioned so that roughly half the points lie above the line and half lie below it, balancing the data evenly on both sides throughout its length.
- Draw a single straight line covering all data points.
- Line should balance points above and below it.
- Line does not need to pass through any points exactly.
Interpreting and Using the Line of Best Fit
The line of best fit summarises the relationship between the two variables and can be used to make predictions.
For example, if you know the value of one variable, you can estimate the corresponding value of the other variable by finding the point on the line of best fit.
However, predictions should be made cautiously, especially when extrapolating beyond the range of the data, as the relationship may not hold outside the observed values.
- Use the line to estimate values of one variable given the other.
- Predictions are more reliable within the range of observed data.
- Be cautious when extrapolating beyond the data range.
Example: Scatter Diagram and Line of Best Fit
Suppose you record the number of hours studied (x) and the marks scored in a test (y) for 7 students: (1, 50), (2, 55), (3, 65), (4, 70), (5, 75), (6, 80), (7, 85).
Plot these points on a graph with hours studied on the x-axis and marks on the y-axis, marking each point with a small cross (×).
The points show a positive correlation because as hours studied increase, marks increase too. Draw a straight line that roughly balances the points above and below it, extending across the data range from 1 to 7 hours. This line is the line of best fit and can be used to estimate marks for other study hours within this range.
- Plot points clearly with crosses.
- Identify positive correlation from upward trend.
- Draw line balancing points above and below it.
At-a-glance summary
Comparison table
| Step | Detail | Example | Exam Use |
|---|---|---|---|
| Plotting points | Mark each data pair on the graph with a small cross (×) | Plot (3, 65) as a cross at x=3, y=65 | Ensure points are distinct and accurate to gain full marks |
| Identifying correlation | Look at the overall pattern of points | Points slope upwards → positive correlation | Use correct terminology: positive, negative, zero correlation |
| Drawing line of best fit | Draw a straight line by eye through the data range | Line balances points above and below, not necessarily through points | Line must cover entire data range for full credit |
| Interpreting line | Use line to estimate values or describe trend | Estimate marks for 5.5 hours study from the line | Explain reasoning clearly to earn marks |
Active recall
Quick check
1. What symbol is recommended to mark points on a scatter diagram?
Small crosses (×) are recommended to mark points clearly.
2. What does a positive correlation indicate about two variables?
It indicates that as one variable increases, the other variable also tends to increase.
3. How should a line of best fit be drawn on a scatter diagram?
It should be a single straight line drawn by eye, covering the entire data set, with roughly equal points above and below it.
4. What does zero correlation look like on a scatter diagram?
Points are scattered randomly with no clear upward or downward trend.