E9.5 Scatter diagrams
- Syllabus
- 0580–2028–2029
- Topic
- E9.5
- Level
- Extended
Learning objectives
E9.5.1Draw and interpret scatter diagrams.• Draw and interpret scatter diagrams.E9.5.2Understand what is meant by positive, negative and zero correlation.• Understand what is meant by positive, negative and zero correlation.E9.5.3Draw by eye, interpret and use a straight line of best fit• Draw by eye, interpret and use a straight line of best fit. Plotted points should be clearly marked, for example as small crosses (×). A line of best fit: • should be a single ruled line drawn by inspection • should extend across the full data set • does not need to coincide exactly with any of the points but there should be a roughly even distribution of points either side of the line over its entire length.
Plot and interpret a scatter diagram
A scatter diagram plots one point for each paired observation, so the overall relationship between two numerical variables can be seen.
Put the explanatory variable on the horizontal axis and the other variable on the vertical axis when the context makes that choice clear. Label both axes with units, use linear scales, and plot each pair as a small clear cross. For (23,31.2), move to 23 on the horizontal scale and 31.2 on the vertical scale; the point must satisfy both coordinates.
Read the whole cloud of points before describing it. State the variables and direction, for example: 'as time in the shop increases, the number of items bought tends to increase.' A point far from the overall pattern is an unusual point; identify it from its coordinates.
Do not join consecutive points. A scatter diagram shows paired observations and a general pattern, not a time sequence or proof that one variable causes the other.
Recognise positive, negative and zero correlation
Correlation describes the direction of the overall relationship between two variables in a scatter diagram.
| Type | Pattern from left to right | Meaning |
|---|---|---|
| Positive | points tend to rise | as one variable increases, the other tends to increase |
| Negative | points tend to fall | as one variable increases, the other tends to decrease |
| Zero | no clear upward or downward pattern | changes in one variable give no consistent direction for the other |
If higher temperature is generally paired with more ice creams sold, the correlation is positive. If greater car power is generally paired with a shorter acceleration time, it is negative. Judge the trend of the whole cloud, not the slope between two selected points.
Correlation can be weak or affected by unusual points, and a very small set may not reveal a reliable pattern. Correlation describes association; it does not by itself prove causation.
Draw and use a straight line of best fit
A line of best fit is a single straight ruled line drawn by inspection to represent the central trend of a scatter diagram.
First identify the direction and centre of the point cloud. Draw one ruled line across the full data set, with roughly even numbers of points above and below it over its whole length. The line need not pass through any point or through the origin, and an isolated unusual point should not pull it away from the main pattern.
To estimate y from a given x, start at the x-axis value, move vertically to the line, then move horizontally to the y-axis and read the scale. Reverse these moves to estimate x from y. An estimate is approximate, so report a precision justified by the scale.
If the best-fit line for two test scores crosses near (40,48), a test 1 score of 40 gives an estimated test 2 score of about 48. The estimate comes from the line, not from choosing the nearest plotted student.
Estimates within the horizontal range of the data are interpolation. Extending beyond that range is extrapolation and is less reliable because the observed pattern may not continue.