Graphical Display

Mastering Graph Scales and the 50% Rule

Understanding how to scale a graph explains why scientists can spot subtle patterns that might otherwise be invisible in a cramped corner of a page. A well-chosen scale spreads the data out clearly to maximize precision.

• Examiners enforce the 50% rule: your chosen scale must ensure that the plotted data points, including any error markers, occupy at least half of the provided graph grid in both the $x$ and $y$ directions.
• You must use a linear scale, which means the axis has regular, consistent increments (e.g., going up in 2s, 5s, or 10s).
• Avoid awkward scales like multiples of 3, 7, or 0.75, as these make plotting difficult and prone to mathematical errors.
• Your graph does not have to start at $(0,0)$. If your lowest measurement is high, you can start the axis at a sensible number near that value, but you must clearly label this new origin.

Plotting Points and Lines of Best Fit

A thick pencil dot might seem harmless, but in a biology exam, it lacks the precision needed to prove your accuracy. Once your axes are set, placing your data perfectly is the next critical step.

• First, use a sharp HB pencil to mark each coordinate with a neat, small 'x' or a cross with a dot. Avoid drawing thick "blobs", as these are penalized for lacking a precise center point.
• Every point must be plotted accurately to within half a small grid square of its true mathematical value.
• If you spot anomalous results (measurements that do not fit the overall pattern), you should still plot them as an 'x', but you must ignore them when determining the trend.
• Draw a line of best fit as a single, thin, continuous line that accounts for the overall trend or correlation of the data.
• Depending on the data's pattern, this will either be a straight line drawn with a transparent ruler, or a smooth freehand curve.
• The line should balance the data, leaving a roughly equal number of points on either side. You must never join the points dot-to-dot.

Indicating Uncertainty with Range Bars

Why do we trust an experiment that has been repeated twenty times more than one that was only performed once? Single measurements rarely tell the whole story, which is why scientists repeat experiments to find the true spread of their results.

• Range bars are added to graphs to indicate the variability of the data around a calculated mean.
• The length of the range bar represents the precision of your measurements; shorter bars indicate high precision because the repeat readings are close together.
• To describe the addition of a range bar: first plot the mean value with an 'x', then draw a straight vertical line passing through this point that extends up to the maximum recorded value and down to the minimum recorded value.
• Crucially, if your repeat readings contain an anomaly, you must exclude it from both the mean calculation and the range bar.
• Measurements also carry uncertainty based on the equipment used. For equipment requiring two judgements (like a ruler), the absolute uncertainty is usually $\pm 1$ of the smallest division.

Worked Example

Calculate the mean and describe how to plot the range bar for the following data on plant stem lengths measured at week two: $42\text{ mm}$, $44\text{ mm}$, $65\text{ mm}$, $43\text{ mm}$.

Step 1: Identify and remove any anomalous results.

• $65\text{ mm}$ is an anomaly because it lies well outside the range of the other repeats and does not fit the pattern.

Step 2: Calculate the mean using the remaining valid data.

• $Mean = \frac{42 + 44 + 43}{3}$
• $Mean = 43\text{ mm}$

Step 3: Determine the maximum and minimum values of the valid data.

• $Maximum = 44\text{ mm}$
• $Minimum = 42\text{ mm}$

Step 4: Describe the plotting process.

• Plot an 'x' at the coordinate for $43\text{ mm}$. Draw a vertical line passing through this 'x' starting at $42\text{ mm}$ and ending at $44\text{ mm}$.