How Charts Mislead: Eight Distortions, Worked on One Real Table

1. The truncated axis, and what it multiplies

Before the arithmetic: East billed 3,040 and West billed 1,685. Work out how many times bigger East is, then look again at the right-hand chart above and say what it appears to claim.

East is 3,040 ÷ 1,685 = 1.80 times West. That is the fact. Now watch what the drawing does to it.

A bar chart works by making length proportional to value, and that only holds if length is measured from zero. Cut the bottom off and the bar no longer represents the value, it represents the value minus wherever you started, which is a different quantity that nobody labelled.

Say out loud why this matters more for bars than for a line chart. A bar's whole job is to be compared by length against its neighbours, so its length must mean something. A line chart's job is to show change over time, and the reader compares slopes rather than distances from the bottom, so a line chart's axis can start somewhere else without the same damage. That is the honest exception, and it is the only one.

The version that catches people out most often is not deliberate. Every charting tool on the market picks axis limits automatically to fill the space, and several of them truncate by default. Nobody decided to exaggerate; the software optimized for filling a rectangle and the reader saw a claim.

2. Percent against percentage point

Before the distinction: a conversion rate goes from 4 percent to 5 percent. Say how much it improved, then notice that you had to pick which of two answers to give.

It rose by 1 percentage point and by 25 percent. Both true, same fact, and the second sounds twenty-five times better. Choosing the flattering one and not saying which you chose is the cheapest distortion available, and it needs no chart at all.

The rule is short. "Percentage points" is the difference between two percentages. "Percent" is the relative change from one to the other. A margin going from 38.6 percent to 40.6 percent gained 2 percentage points, or about 5 percent. Say which one you mean, every time, and prefer showing both rates side by side, because two rates cannot be misread.

This one is worth a slightly harder line than the others, because unlike a truncated axis it produces no visual clue at all. The reader has nothing to check.

3. The cherry-picked window, and the missing month

Before the numbers: here is our monthly revenue. Pick the two-month window that makes the business look best, then the one that makes it look worst, before reading on.

January   2,630
February  2,245     -14.6% against January
March     2,585     +15.1% against February
April         0     no orders at all
May       2,430      -6.0% against March

February to March is up 15.1 percent. January to February is down 14.6 percent. January to May is down 7.6 percent. Every one of those is a true statement about the same four numbers, and each supports a different story. Nothing in the chart tells the reader which window was chosen or why.

The defence is not complicated: show the whole series you have, and if you must truncate it, say where the data starts and why. A chart that begins at a local low point is making a claim about the choice of start date that it has not stated.

Then there is April, which is the more interesting problem. There are no April orders. If you group by month and chart the result, most tools will draw four bars, January February March May, evenly spaced, with no gap. A reader looking at that chart sees a stable business. A calendar with a real April in it tells a different story.

A missing period is the one distortion that happens entirely by accident and misleads entirely by omission. Every month with no rows silently vanishes from a grouped result, which is why the fix is a date table joined to your data rather than anything to do with the chart. That mechanic is worked through in month-over-month in Excel and the SQL version.

4. Shares that hide the total

Before the example: East is 30.7 percent of revenue and West is 17.0 percent. Say what those two numbers do not tell you, before reading on.

They do not tell you whether the business grew. A share is a ratio, and a ratio can move because its numerator moved, because its denominator moved, or because both did. East's share could rise while East's revenue falls, as long as everyone else falls faster.

Here are our four regions both ways.

A chart of the share column alone is not wrong, and it is incomplete in a specific way: it always adds to 100 percent no matter what happened to the business. Put the total somewhere on the chart, in the title if nowhere else. "Revenue by region, 9,890 total" costs seven characters and closes the gap.

5. Pie charts, and what angles cost the reader

Before the comparison: picture our four regions as a pie. Now picture them as four bars. Decide which one lets you rank South against North faster, before reading on.

The bars, and it is not close. South is 27.0 percent and North is 25.2 percent, a gap of 1.8 points. As bar lengths that is visible. As pie slices it is a difference of about six degrees of arc, and people cannot read six degrees.

This is not a matter of taste. Judging position along a common scale, which is what a bar chart asks of you, is something people do accurately. Judging angle and area, which is what a pie asks, is measurably worse, and the gap widens as the number of categories grows. That ranking of visual tasks is one of the most reproduced results in the field, and it is in the "why this works" section below.

Where a pie is fine: two or three categories, where the point is that something is roughly half or roughly a quarter, and nobody needs to rank anything. Where it fails: five or more slices, slices of similar size, comparing two pies to each other, or any pie exploded or tilted.

Now picture the last pie chart you saw in a deck. How many slices did it have, and could you have put them in order without reading the labels?

6. Area and 3D: doubling a length quadruples the ink

Before the arithmetic: you replace bars with pictures of desks, and you want one desk to represent twice as much as another. You scale the picture to twice the height, keeping it in proportion. Say what the reader sees, before reading on.

They see something four times as big, because scaling both the height and the width by 2 multiplies the area by 2 × 2 = 4. The same trap catches circles: double the radius and the area goes up four times. A "bubble" chart where the bubble's radius is set to the value overstates every comparison, and correctly built bubble charts scale the area instead.

Three-dimensional bars and pies have the same problem with an extra layer. A 3D pie is tilted, so the slices nearer the front are drawn with visible depth and take up more of the image than their angle deserves. The slice at the front of a tilted pie can look half again as large as an identical slice at the back. There is no reading of a 3D chart that recovers the numbers, which is the reason to have no 3D charts.

The rule that covers all of this: encode value with one dimension, and let the other stay constant. Bars have equal widths for a reason.

7. Dual axes, and the correlation you drew yourself

Before the problem: you plot revenue and order count on one chart with two different value axes, one on each side. Say who chose where those two axes start and end.

You did, or your tool did on your behalf. And that choice decides whether the two lines appear to track each other, cross, or diverge. Slide one axis and the same two series can be made to look tightly linked or completely unrelated. Whatever relationship the reader perceives was authored, not measured.

Dual axes are not banned, and they are the wrong default. Three alternatives, in the order I reach for them:

Two charts stacked, sharing the same time axis. The reader compares shapes, and no false relationship is manufactured by scaling.

Index both series to 100 at the start of the period. Now they are on one axis honestly, and the chart shows relative change, which is usually the actual question.

Chart the ratio itself. If revenue per order is what you care about, compute it and plot one line.

If you do use a dual axis, say so plainly in the title or subtitle, and never use one to imply causation. The general version of that mistake is in correlation vs causation, and a dual-axis chart is where it is most often committed with the best intentions.

8. Log scales: honest, and easy to misread

Before the case: your data runs from 100 to 10,000. On a normal axis, the small values are all squashed into a strip at the bottom. Say what a log scale changes, before reading on.

A log scale spaces values by ratio rather than by difference. Equal distances mean equal multiplications, so a tenfold rise always occupies the same height whether it is 100 to 1,000 or 1,000 to 10,000.

values:      100    300   1000   3000  10000
linear gaps:      200    700   2000   7000     <-- wildly uneven
log10 gaps:     0.477  0.523  0.477  0.523     <-- near enough equal

That makes a log scale the right choice for anything spanning several orders of magnitude, and for anything where a percentage change is the interesting quantity. A constant growth rate is a straight line on a log scale and a curve on a linear one.

The misleading part is that most readers do not notice they are looking at one. On a log axis, a doubling looks modest and a curve that is exploding looks tame. Label it clearly, mark the axis with round multiples like 100, 1,000, 10,000, and say "log scale" in the subtitle. A log scale is honest and it needs a sign on it.

Edge cases and honest exceptions

Six, including the cases where a rule bends.

Line charts may start above zero. The reader is judging slope, not length, and forcing zero on a stock price or a temperature series flattens the thing you are trying to show. Label the axis clearly and it is fine.

Data that cannot be zero. Body temperature, pH, a year number. Zero is not a meaningful baseline and forcing it produces a chart of nothing. Use a scale that fits the plausible range and say what it is.

Sorting alphabetically when the question is ranking. Not a distortion exactly, and it costs the reader the entire finding. Sort by the value being compared unless the categories have a natural order like months.

Colour doing work it cannot do. Around one man in twelve has some form of red-green colour deficiency, so a red-versus-green chart is unreadable for a meaningful share of any audience. Use position, labels or lightness for anything essential.

Averages drawn without spread. Four bars of group averages look like four facts. If one of them rests on three rows it is not one, and the chart gives no clue. This is the visual version of the problem in mean vs median.

Precision that is not there. A chart labelled to two decimal places on data with a wide interval is claiming a measurement it does not have. Round to what you can defend.