Presenting Results

A graph is not decoration. It is the analysis: it shows the relationship, exposes anomalies, and lets you extract a quantity that no single reading contains.

Which variable goes where — the independent variable on the x-axis, the dependent variable on the y-axis. Depart from this only when you are deliberately rearranging to get a straight line.

Labelling axes — every axis carries the quantity and its unit, written as quantity / unit, for example extension / mm. Written that way the axis numbers are pure numbers, which is exactly what they are.

Choosing a scale — the plotted points should fill at least half the grid in both directions. A graph squashed into one corner wastes the resolution you took the trouble to measure at, and makes the gradient far harder to read accurately.

Sensible scale intervals — use 1, 2, 5 or 10 units per large square. Awkward intervals such as 3 or 7 per square cause plotting mistakes, and every misplotted point is an anomaly you invented.

Example: readings from 0 to 47 mm plotted with 5 mm per square fill the paper and are easy to read. The same readings at 10 mm per square use half the page, and at 3 mm per square invite arithmetic errors on every point.

The origin is not compulsory — include it when you need the intercept or want to demonstrate proportionality. If the data sit between 200 °C and 240 °C, forcing the axis to start at zero compresses all the variation into a thin band and hides it.

Plotting points — a small, sharp cross or a dot with a circle, accurate to better than half a small square. Fat pencil blobs discard precision you have already paid for.

Line of best fit — a smooth line, straight or curved, with roughly as many points above as below and the residuals balanced along its length. It does not have to pass through any particular point, it should not be forced through the origin, and it must never be a dot-to-dot.

Error bars — a bar through each point spanning its uncertainty shows the reader how much confidence each reading deserves. If the uncertainty differs from point to point, the bars differ too, and that in itself is informative.

Curves — when the relationship is not linear, draw the curve freehand and smoothly rather than joining points with straight segments. A physical relationship rarely changes direction abruptly, and a jagged line suggests structure in the data that is not there.