Learning outcomes
- Choose sensible graph scales.
- Label axes with quantity and unit.
- Plot points accurately.
- Draw a best-fit line or smooth curve.
- Identify anomalies without forcing the line through them.
9.1 Choosing axes
Plot the independent variable on the horizontal x-axis and the dependent variable on the vertical y-axis unless instructed otherwise. Label each axis with quantity or symbol and unit using the same convention as the table.
Do not write only the unit or only a number scale. A graph of temperature against time should have time / s on x and temperature / °C on y.
9.2 Scale selection
Scales should use more than half of the available grid in both directions. Use simple steps based on 1, 2 or 5 multiplied by powers of ten. Avoid awkward increments such as 3 units per large square because they increase plotting errors.
The origin need not be included unless physically relevant or required to judge proportionality. A false origin may be used when all data occupy a narrow non-zero range, but mark it clearly.
9.3 Plotting points
Plot to the nearest half-small-square. Use small crosses, plus signs or clear encircled dots. Large blobs hide the true coordinate and reduce accuracy.
Check each point by reading back to both axes. A common error is to reverse coordinates or use a table row from the wrong column.
9.4 Best-fit line or curve
A best-fit straight line is a single thin line drawn by inspection so that the scatter is roughly balanced above and below over the full range. It does not need to pass through every point.
If the trend is curved, draw a smooth curve rather than joining point to point. Point-to-point zigzags imply sudden physical changes unsupported by the experiment.
9.5 Anomalies
An anomaly lies clearly outside the general pattern. Circle or identify it if appropriate and ignore it when drawing the best-fit trend, but do not classify ordinary scatter as anomalous.
Consider whether the anomaly arose from a reading or recording mistake. If practical time permits, repeat that measurement at the same independent-variable value.
Worked examples
Scale choice
Data from 0.12 A to 0.68 A can use 0 to 0.70 A with 0.10 A per major interval. This is easier and uses the grid better than 0.03 A per interval.
Best fit
With seven points scattered around a straight trend and one isolated point, draw the line through the main distribution, not from first point to last point and not through the anomaly.
Practical focus
Investigation or training activity
Plot the same dataset twice: once with a poor compressed scale and once with a suitable scale. Compare the ease of detecting scatter, anomalies and gradient.
Examination guidance
- Use at least half the grid in each direction.
- Use simple scales.
- Label axes with quantity and unit.
- Use small precise point symbols.
- Never join experimental points dot-to-dot unless specifically asked.
Check your understanding
- Which variable usually goes on the x-axis?
- Must every graph start at zero?
- How should a best-fit line relate to scatter?
- What should be done with a clear anomaly?
Answers
- The independent variable.
- No, unless the origin is relevant or required.
- There should be a roughly even distribution of points above and below.
- Identify it, investigate or repeat it, and do not force the line through it.
