A number is a claim with the argument removed

Numbers persuade because they look like they have stopped being opinions

“Sales grew 50%” reads as a fact. It is a fact about a ratio between two numbers, both of which somebody chose, over a window somebody chose, measured by a definition somebody chose. All three choices are arguments, and all three are invisible in the sentence.

This matters in two directions. You will be handed numbers by clients and you have to make them into something honest. You will also be tempted, every time, by the version that sounds better.

Always give the denominator

The commonest failure is a percentage without a base. “A 50% increase in customers” is two customers becoming three. “Doubled our reach” is 400 people becoming 800. Neither is dishonest until it is used to imply scale it does not have.

The repair is a habit rather than a judgement: state the absolute and the relative in the same sentence.

“From 2 in every 1,000 to 3 in every 1,000: a rise of 50%.”

That sentence is harder to misread in either direction. A reader who wants the alarming version and a reader who wants the reassuring version both have to look at the same two numbers. Medical and risk communication has converged on this construction for exactly that reason: relative change alone systematically inflates how large an effect feels, and absolute change alone can bury one that matters.

Three windows, three different truths

Ask anybody for a growth figure and they will give you the window that flatters. This is rarely deliberate; the flattering window is the one they remember.

• Measured from the worst month, everything is a recovery.
• Measured from the launch, everything is growth.
• Measured year on year, seasonal businesses stop lying to themselves.

The working rule is to state the window in the same breath as the number, and to prefer a window chosen for a reason you can say out loud: a full year because the business is seasonal, since the new premises because that is the change being discussed. If the number only works in one particular window, you have found something out about the number.

The chart is an argument too

A line chart makes three editorial decisions before anyone reads it: where the vertical axis starts, how wide the time span is, and what is left off.

• A truncated vertical axis (starting at 94 rather than 0) magnifies small changes into cliffs. There are legitimate uses, mainly where zero is meaningless, such as body temperature or a stock index. There is no legitimate use on a bar chart, because a bar encodes quantity by length, and a bar cut off at the bottom is drawing the wrong length.
• Squeezing the horizontal axis steepens every line. Two charts of identical data at different widths tell different stories, and neither is false.
• What is missing is the hardest to see. A chart of surviving businesses is a chart with the failures deleted, and the shape it draws is the shape of survival, not of outcome.

Check the definition before you draw anything

“Customers” can mean accounts, people, households, or orders. “Active users” depends entirely on a period somebody picked. “Response time” can be a mean, which one bad week ruins, or a median, which hides the bad week entirely.

Ask two questions of every number you are given: counted how, and from what? A surprising proportion of the time the person supplying the figure does not know, and finding out changes it. That is not an obstacle to the work; it is the most useful hour you will spend on it, because the number that survives the question is the one you can put on a wall.

The free path is complete

You do not need paid software for any of this. LibreOffice Calc and Google Sheets do the arithmetic. Datawrapper’s free tier produces clean, accessible, embeddable charts and defaults to sensible axes. For anything programmatic, Python with pandas and matplotlib, or R, cost nothing and are what most published analysis is actually made with. If you are on a phone, Google Sheets and Datawrapper both work in a mobile browser.

Where this stops being technique

There is a line between choosing a clear presentation and choosing a flattering one, and it is not always obvious where you are standing. A usable test: would you be comfortable if the audience saw the other defensible presentation next to yours? If the answer is no, you have not designed a chart, you have built an argument that depends on the alternative being hidden.

The honest limitation is that no presentation is neutral. Every chart has an axis, a window and an omission, and a person who says their version is the data is either inexperienced or selling something. What you can do is make your choices visible (label the axis, state the window, say what is excluded) so a reader can disagree with the framing rather than only with the conclusion.