Beyond the Axes: How Scale Choices Can Shape Visualisation

The idea of scale is at the heart of data visualisation. Why? Because numbers alone have no inherent sense of magnitude. They have, in other words, no sense of their own size—this sense of size is instead projected onto them by us and depends heavily on context.

Think of it this way—how big is an increase of 200? If it were your heart rate, a jump of 200 would warrant an immediate trip to the ER. But if it were your annual income, the change would barely register—it would be more like a rounding adjustment than a meaningful bonus.

Visualising the Impact of Scale Choices
In daily conversations, language provides context, giving us an intuitive sense of scale and relativity when we speak about numbers.

In visualisations, however, this context is shaped by the decisions we make. Choices
like setting axis ranges, choosing appropriate units of measurement, or determining the aspect ratio of a graph can all have a surprisingly significant impact on the story the data conveys.

To understand how these choices influence our perception of data, let us explore an example.

A Tale of Two Graphs: How Outliers Influence Perception
Say I am looking at the average price of milk over time. In the month of July, we have some severe supply chain disruptions due to a drought affecting dairy farms, and the average price shoots up to $10.

These prices are plotted in the time series below:

According to this graph, prices were relatively stable and varied little before and after July. There was only one significant fluctuation, and that was in July when the average shot up to $10.

But this is not necessarily the case, and it is not the only story that could be told using this data. Including the month of July has forced us to adjust the y-axis scale, instead of the y values running from 0 to $2.50, they now run from 0 to $11 instead — to accommodate the outlier.

Removing the outlier and plotting the prices on a smaller scale will magnify smaller changes instead, creating a much more volatile picture of the prices than what is seen above:

The Expanded Y-Axis: When Big Numbers Hide Small Changes

Why does this happen? Well, it is not due to any actual change in the values themselves— we’re using the exact same dataset, just with the outlier removed. The effect is called an expanded y-axis, and it occurs because a larger scale diminishes the visibility of smaller fluctuations.

In our example, the July outlier (a sharp spike in price) forces the scale to stretch to
accommodate the broader range, effectively compressing smaller variations into a less noticeable portion of the graph. As a result, subtle but potentially important changes in price become nearly invisible.

The Compressed Y-Axis: Magnifying Minor Fluctuations
Naturally, then, a compressed y-axis, with a smaller than necessary range, will have the opposite effect. The y-axis becomes overly sensitive, and even minor fluctuations are magnified, making them seem more significant than they really are.

Say we removed the outlier and plotted the changes in price (in dollars) over the various months instead — though it may not occur to us at the time, here we are forced to make a certain decision: what do we consider to be a significant price difference?

Below, we see two graphs: in the left-most graph, the y-axis caps at 0.80, reflecting the largest price difference in the dataset—80 cents. In the right graph, the y-axis extends to
$2; let’s say this is because $2 represents a threshold where price changes might become noticeable or significant to consumers.

In this case, the graph on the left could be considered an example of a compressed y- axis, where overly narrow range exaggerates normal fluctuations that are not
necessarily of importance, creating the impression that they matter more than they actually do.

In our example, the only changes of significance are at the $2 threshold, and the broader range of the right-hand graph provides a more accurate representation of what matters to consumers, avoiding unnecessary emphasis on minor variations.

High-Range Datasets: The Challenge of Variability
But removing outliers or adjusting the y-axis scale is not feasible with every dataset. In high-range datasets, an expanded y-axis is often still necessary to accurately represent the full range of data.

However, this can highlight a fundamental mismatch between the scale of the data’s range and its variability. The broad span of values may obscure smaller but potentially significant fluctuations, masking potentially important trends.

Take housing prices for example: while prices in a city might span from $200,000 to
$5,000,000, changes in price tend to be much smaller. If the y-axis was scaled to cover the entire range, these smaller fluctuations would become nearly invisible, making it harder to identify meaningful trends in price growth or decline.

Data Transformations: Unlocking Hidden Trends
It is here in high-range datasets where data transformations truly prove their value.

Transformations, such as taking the logarithm of the values, reduce the range of the data while maintaining the proportional relationships between them. This compression of scale enables clearer visualisation of smaller fluctuations without losing the broader context.

See below the yearly percentage change in house prices for three Victorian suburbs, plotted with and without transformation.

Note how in the untransformed graph, what dominates is the sharp increase and subsequent drop-in growth rates for St Leonards. However, Fitzroy displayed a similar drop from 2017 to 2018 and that is practically invisible until we adjust the scale. By transforming the data, smaller fluctuations become more noticeable alongside the other data points, revealing trends that were previously obscured.

Aspect Ratios: The Shape of Your Data Story
There are many more ways in which choices around scale can obscure the clarity of data visualisations, but the last I will consider here is aspect ratio. Much like the others, this error can creep in unnoticed, as it’s often a decision left to default software settings.

Programs like R Studio are not always optimised to select the most appropriate aspect ratio, and an incorrect ratio can stretch or compress the visual representation, distorting trends and making fluctuations appear more or less significant than they truly are.

Choosing the Right Aspect Ratio for Your Data
Broadly speaking, aspect ratios can be categorised into wide, square, or tall.

A square (1:1) aspect ratio is best for datasets where both axes have comparable ranges and where the relationship between variables is equally important in both dimensions— such as in scatter plots comparing two variables.

A wider aspect ratio (more horizontal than vertical) is usually suitable for time-series data, where the focus is on trends over time, allowing for more space to show how data evolves across the x-axis without distorting the time intervals.

A tall aspect ratio is typically useful when y-axis values have a larger range and need more vertical space to highlight variations.

But be careful, sometimes data has several considerations.

For example, in time-series plots with multiple datasets, a taller aspect ratio may be necessary to clearly display variations across datasets with different value ranges.

This is because a taller aspect ratio provides more vertical space, making it easier to distinguish trends and fluctuations in each dataset. Without this adjustment, the data can appear compressed, obscuring meaningful patterns.

A taller graph ensures that each dataset’s range is properly represented, improving clarity and interpretation.

Compare, for example, this wide format of a graph displaying the World Economic Forum’s gender gap index over time:

With this tall format below:

In the wide format, the subindices are compressed, making their trends appear more uniform and less distinct. The taller format, however, stretches the y-axis, providing more vertical space to highlight the unique trajectories of each subindex.

Scale as the Lens of Insight
In conclusion — whether it’s adjusting the y-axis scale, refining the aspect ratio, or transforming the data itself, scale is far more than just setting the bounds of your axes.

It acts as the lens through which we frame our data, providing context, enabling meaningful comparisons, and uncovering hidden patterns—or, when misapplied, distorting the truth, and leading to misrepresentation.

Scale shapes not only how we view the data, but also how we derive meaning from it and understand its narrative.

By applying scale responsibly and with intent, we ensure our visualisations do more than accurately represent the data, illuminating the insights that actually matter.