The field guide
64 ways a chart can mislead
The techniques that do most of the misleading, grouped by type. Each page explains how the technique works, how to spot it in the wild, and what an honest version of the chart looks like.
Axis crimes
Where most chart lies begin: the humble axis, bent until the data confesses.
The truncated axis
A 3% difference, presented as a landslide.
Bar charts encode value as length, so the baseline has to be zero — chop the bottom off the axis and a bar twice as tall no longer means twice as much. Start the axis at 94 and a one-point gap reads as total domination.
7 exhibits in the gallery
Dual y-axes
Two axes, one narrative, infinite flexibility.
Put one series on the left axis and another on the right, and you get two free knobs to turn until the lines cross exactly where the story needs them to. The correlation you “see” is a design decision, not a finding.
3 exhibits in the gallery
The inverted axis
Up is down. Less is more.
Flip the y-axis so larger values plot lower, and every trend reads backwards. Famously used to make a rise in gun deaths look like a decline — at a glance the chart says the exact opposite of its own numbers.
3 exhibits in the gallery
Uneven intervals
1990, 1995, 2000, 2004, 2006, 2007 — evenly spaced.
Plot irregular time steps at regular spacing and you silently stretch some periods and compress others. Slopes become fiction: a decade and a single year occupy the same width, so the “acceleration” is typography.
5 exhibits in the gallery
The log scale
Every gridline is another ×10, and the eye reads them as equal steps.
A log axis spaces equal ratios equally: 1 to 10 occupies the same width as 1,000 to 10,000. For data that genuinely spans orders of magnitude that is the right tool — but the eye still reads distance as amount, so a thousandfold gap arrives on the page looking like a modest lead. Put bars on one and it gets worse: a bar encodes its value as length from zero, and a log axis has no zero, so every bar’s length is set by wherever the axis was started. And what the axis has no zero for it has no room for either: the logarithm of zero is undefined, so a row worth nought is not drawn small, it is not drawn. That one is the quietest failure in the family, because it takes a row out of the table rather than bending the scale — on a line chart the point vanishes and the line closes over the hole, and widening the axis will never bring it back.
2 exhibits in the gallery
The broken axis
The zero is still there. The middle is missing.
A truncated axis chops the bottom off the scale and announces itself by starting at 94.6. A break does something quieter: it keeps the zero, keeps the top, and takes a slice out of the middle, marking the theft with a small zigzag most readers have been trained to read as a tidying-up. What it removes is not empty space — it is the part of the scale where the difference between the bars actually lives, so lengths on either side of it stop meaning the same thing and the ratio between any two bars becomes whatever the designer’s choice of gap made it. Worse, the two halves are almost never drawn at the same rate: the compressed top buys room for the giant, and every unit up there is worth a fraction of a unit down below.
1 exhibit in the gallery
The clipped axis
Everything taller than the frame is drawn exactly as tall as the frame.
A truncated axis takes the bottom of the scale and a broken axis takes a slice out of the middle. This one takes the top, and it is the quietest of the three, because nothing about the axis looks wrong: the zero survives, the ticks are round, the gridlines are evenly spaced, and there is no zigzag to mark the theft. What has gone is the range above the last tick. The maximum was fixed — a dashboard setting, a target line, a template, a limit typed once and never revisited — and the data was never asked whether it fitted. Every value that runs past the top is drawn at the top, so above the ceiling the mark stops being a measurement and becomes a threshold test: all quantities up there are the same quantity. How it fails depends on the mark — bars, columns, gauges and clamped colour scales arrive flat against the frame, while a line simply leaves it and comes back, which is louder but just as unmeasurable. And unlike the other two, it leaves the reader nothing to work with, because what it removed is not on the chart to be noticed — a truncated axis at least prints the number it starts at, while a ceiling’s whole effect lives in values the picture never mentions.
2 exhibits in the gallery
The aspect ratio
Same numbers, same axis, same range — and the slope is whatever shape the box is.
Every angle on a chart is two exchange rates divided by one another: how many pixels the vertical axis gives a unit of data, over how many the horizontal axis gives a step of time. The labels declare the two ranges and never the shape of the box those ranges are drawn in, so one series, on one scale, over one span, can be squeezed into a tall panel and read as a collapse or stretched into a wide one and read as a drift, with no number moved and no baseline chopped. It is the axis crime that survives a zero baseline, because it is not about where the axis starts but about how far apart the two axes have been pulled — and it is almost never a decision. A dashboard tile, a column width, a slide template, a figure resized to fill the space left over: the container picks the drama, and the caption never mentions that it did.
1 exhibit in the gallery
The rebased index
Every line passes through 100 on a date somebody chose.
Indexing divides every series by its own value in one chosen period and multiplies by 100, which is why it is the standard cure for dual axes: two quantities of different size, in different units, end up on one honest ruler. The cure has a knob. Each series is divided by a different number, so moving the base multiplies each line by a constant of its own — one slides up, the other down — and the gap the reader carries away is a fact about the date in the divisor as much as about the data. The base is also the single point where the chart declares the series equal, so the crossing everybody reads off is a cell in a spreadsheet. And the reading inverts either side of it: to the right of the base the higher line has grown more since the base, while to the left the higher line is the one that grew less on the way to it.
2 exhibits in the gallery
The logarithmic unit
The axis is linear. The unit is already a logarithm.
A log axis at least announces itself: the ticks read 1, 10, 100, and a reader who looks can see what was done. This one hides a step earlier, inside the measurement, where no axis setting can reach it. pH, the decibel, earthquake magnitude, stellar magnitude, the f-stop and the semitone are not quantities but logarithms of quantities, agreed on long ago precisely because the numbers underneath span too many orders of magnitude to carry around. Plot one on a perfectly ordinary linear axis and that axis is quietly doing what a log axis does: equal distances are equal ratios, so every gap the eye measures is a multiplication and no difference on the chart is an amount. Three things follow, and each of them survives an audit. Adding logs multiplies the quantities, so a mean of pH readings is the geometric mean of the acid rather than the arithmetic one, and a gap quoted in “points” is a ratio rather than an amount. A curve that flattens has not slowed down — it has stopped multiplying as fast, while the quantity underneath can be accelerating, and the flat stretch is often where most of it arrives. And several of these units carry a minus sign as well, so the line falls while the thing it measures rises. Unlike a truncation, none of it can be fixed by widening the range: draw the pH from zero, or across the whole 0–14, and the picture is flatter rather than fairer, because the compression lives in the unit and not in the frame.
2 exhibits in the gallery
The auto-ranged axis
Both ends fitted to whatever is on screen, so every window is equally dramatic.
The other axis crimes are decisions. Somebody chose a floor, typed a maximum, cut a slice out of the middle; a reader who looks can see what was done and, in the first two cases, roughly undo it. This one is what happens when nobody chooses. Both ends of the scale are computed from the data currently in view, so the series fills the frame by construction and the amplitude on the page stops carrying information: a two-unit wobble and a fifty-unit collapse arrive at very nearly the same height, and the quieter the data the harder the axis zooms until the last digit of the instrument is a mountain range. The near relative is the free-scale panel grid, and the two are worth telling apart, because they are one rule applied along two different directions: there, several series sit side by side and each panel is given a ruler of its own, so at least the grid is visible and a reader who checks the axes can catch it. Here it runs along time instead. One series, one panel, one place on the dashboard — and a different ruler every time anybody looks at it, with nothing on screen to compare against. Three consequences follow, and none of them is visible in the picture. The exchange rate between a unit of data and a millimetre of screen is recomputed every time the window moves, so two pictures of one series are not comparable and the change you remember seeing is not one you measured. The scale is recentred as well as resized, so a level difference between two panels — often the actual finding — appears on neither of them. And both ends are set by the two most extreme points in view, so a single spike, a sensor glitch or one flush of a line decides how everything else in the window is drawn.
2 exhibits in the gallery
The padded axis
The frame is the size of the unit. The data is the size of the data.
The truncated axis raises the floor and makes a small difference enormous. This one is the same decision taken at the other end of the scale, and it makes a large difference invisible: the baseline is honest, the ticks are even, nothing is broken or clipped, and the top of the axis was chosen from the unit rather than from the numbers. A percentage runs to a hundred, so the axis runs to a hundred. A score runs to ten, a rating to five, a dial to whatever the face was printed with, a meter to its full-scale deflection. The data then lands in the first few per cent of the frame, and everything above it is a wall of empty box. What makes this one slippery is that the arithmetic is untouched. Bars from zero keep their ratios exactly: a model that fails twenty-eight times as often really is drawn twenty-eight times as tall, and anybody who measures the ink with a ruler gets the right answer. But nobody measures the ink. The eye reads each mark against the frame and against its neighbours, and when the whole field is a row of stubs along the floor, a twenty-eight-fold range arrives as a handful of pixels — below the size at which two lengths can be told apart by looking at them, which is where comparison actually happens. The conclusion the picture delivers is that nothing here is adrift, the variation is noise, the choice does not matter; and that conclusion was written by the empty space rather than by the data. It is most at home wherever the interesting quantity is rare — failure rates, fraud rates, defect rates, error rates, anything counted in parts per something — because rare things live near the bottom of their unit by definition, and the tool that drew the chart has no way of knowing that the bottom is where the whole story is. Four neighbours are worth telling it apart from, and the closest in outcome is the bar with no true zero, which produces the same wall of identical bars and takes the same cure — a dot plot and a unit people act in. The difference is where the damage is. There a constant sits inside every bar, so the ratios between them are wrong and subtracting the origin fixes it; here the ratios are exactly right and merely too small to see, so nothing needs recomputing and only the frame moves. The other three are about the frame as well. The clipped axis puts the ceiling below the data and flattens what pokes through; this one puts the ceiling far above it and flattens everything. The auto-ranged axis takes both ends from the data every time it is drawn, so every window is equally dramatic; this is the same abdication running the other way, and between the two of them sits the honest thing nobody did, which is to choose the bounds once, from the question. And the truncated axis is its mirror: raising the floor manufactures drama, padding the ceiling erases it, which is why the padded axis tends to turn up in charts that want a reassuring answer rather than an alarming one.
2 exhibits in the gallery
Size & scale
When 2× somehow looks like 8×. Your eye reads ink, not numbers.
The area illusion
Twice the value, four times the ink.
Scale an icon’s or circle’s height by the data and its area grows by the square. A value that doubled looks quadrupled — and in 3D, octupled. Your eye judges the ink, not the radius.
6 exhibits in the gallery
Gratuitous 3D
The slice in front always wins.
Tilt a pie chart into 3D and perspective inflates whatever sits closest to the viewer, with a thick rim thrown in as bonus ink. 3D bars pull the same trick with parallax — nobody can tell where the tops actually are.
3 exhibits in the gallery
The impossible pie
70% + 63% + 60% = one pie chart.
A pie chart promises that its slices sum to a whole. Feed it multi-select survey data — where respondents could pick several answers — and you get confident-looking slices adding up to 193%.
2 exhibits in the gallery
The radar chart
A spoke twice as long paints four times the ink.
A radar chart asks you to judge a row of numbers by the area of the shape they enclose, and area grows as the square of every spoke — so a modest lead in the scores arrives on the page as a commanding blot. Two more knobs hide in the same picture: the radial axis is rarely zero-based, which stretches the spokes before the squaring even starts, and the enclosed area depends on which categories happen to sit next to each other, so reordering the labels changes the shape without changing a number.
2 exhibits in the gallery
The false common scale
Same word on the axis. Not the same thing being counted.
A bar chart makes exactly one promise: that its lengths are commensurable, because every one of them is so many of the same thing. Put rows on it whose unit quietly changes — counts of objects that do different jobs, figures collected under different rules, quantities that happen to share a word — and the promise is void while the picture looks unchanged. Nothing is exaggerated and no axis is bent; the ranking is simply about a quantity that does not exist.
2 exhibits in the gallery
The bar with no true zero
The axis starts at zero. The quantity doesn’t.
Every other baseline crime in this taxonomy is about the axis. This one is about the unit, and it survives the audit that catches the others: the axis genuinely starts at zero, the ticks are even, nothing is broken or clipped, and each bar is exactly proportional to the number beside it. The number is the problem. A bar says “this much of the thing”, which only works if the thing runs out at zero — and plenty of everyday measures do not. A ratio of a total to one of its parts cannot go below 1. An index is 100 at its base by construction. Degrees Celsius put their origin at the freezing point of one substance, and IQ has no origin at all. Draw any of them from zero and the distance between the axis and the quantity’s real origin is added, identically, to every bar — a constant the data can never move, drawn to scale, usually taking up most of the ink. Which way it lies then decides which way the chart is wrong, and it goes both ways. Where the drawn zero sits below the true origin, the constant pads every bar and every ratio is squeezed toward 1: a fleet whose worst site wastes nearly four times what its best one does arrives as a row of bars a tenth apart. Where the drawn zero sits above it, the padding is negative and ratios blow up instead, which is how 20 °C becomes “twice as warm” as 10 °C when in absolute terms the two differ by 3.5%. Either way the length has stopped being the quantity, and the giveaway is that the subtraction needed to fix it is often printed on the page already, down in a footnote, because whoever quoted the comparison in words could not get a sensible number out of the axis either. Two neighbours are worth telling it apart from. “The logarithmic unit” is the same shape of crime — the distortion lives in the measurement rather than in the frame — but there the unit is a logarithm, so distances are ratios and no amount of subtracting will fix it; pH and the decibel belong to both pages, with the offset the smaller of their two problems. “The rebased index” owns the question of which base year to pick; this page owns what happens when an index is then drawn as a bar, since every one of them carries a 100 that no series can move.
2 exhibits in the gallery
The stack with one baseline
One band starts at zero. The rest float on whatever is underneath them.
Stacking pours the series into one silhouette, and only the one at the bottom keeps a baseline. Every band above it is the gap between two moving edges, so reading one means subtracting two positions the chart never prints — and where the stack climbs steeply the eye measures the shortest way across the band rather than the vertical way, which shaves it thinner still. Then there is the variant that runs the axis to 100%, and it is the one that does real damage: the total is divided out, so nothing on the page is an amount any more. A series that tripled can only be drawn as a narrowing band if the series beneath it grew faster, and narrowing is what the reader remembers.
2 exhibits in the gallery
The word cloud
The biggest word is usually just the longest one.
A word cloud asks the eye to rank quantities by how big the words look, and a word’s size on the page is set by two things, only one of which is the data. The font size carries the frequency; the letter count carries nothing at all. A word’s footprint is its em square repeated once per letter, so what the reader actually measures is frequency times length — and an eleven-letter word at half the count reliably outdraws a three-letter one. Even the charitable sizing rule, font size set to the square root of the count, which is trying to make area track frequency, only ever governs one of the two dimensions. Around that sit the knobs nobody declares: a stop-word list that decides which words exist at all, a layout seed that rearranges the picture on every run, rotation that shrinks whatever it turns, and colour that usually means nothing while the eye goes on looking for its meaning.
1 exhibit in the gallery
The map projection
Greenland is not bigger than Africa. The map is.
A globe cannot be flattened without something being stretched, and every projection chooses what it will sacrifice. Web Mercator — the one under nearly every map on the internet — keeps angles and local shape, and pays for it in area: it stretches both directions by the secant of the latitude, so it stretches area by the square of that. Every square kilometre is quietly multiplied before you see it, by 1 at the equator, 2 at 45°, 4 at 60° and 33 at 80°, and the eye reads the ink rather than the coordinates. The same arithmetic escapes the picture and turns up as a figure with units on it, because a GIS asked for an area in the coordinate system it happens to be drawing in will answer in square metres of the projection plane and never mention that the plane is not the ground.
1 exhibit in the gallery
The treemap
Thirteen rectangles, no axis, and one area judgement per comparison.
A treemap gives every value a rectangle whose area is exactly proportional to it, and then packs the rectangles together. The arithmetic is impeccable and the job it hands the reader is the hardest one on any chart: area is the product of two dimensions, so nothing you can measure on the page is the value. A tile can be the widest on the chart and the fifth largest, because width is only half of it. There is also nothing to measure against — no axis, no baseline, no gridlines, only neighbours — and the shapes are not even fixed by the data: feed the same numbers to the same layout in a different order and every rectangle changes proportions while its area stays put.
1 exhibit in the gallery
The free-scale small multiple
Six panels in one grid, six different rulers.
A small multiple works by holding everything constant except the data: same chart, same size, same years, same scale, repeated down the page, so that any difference the eye finds is a difference in the numbers. Fit each panel’s axis to its own series and the last of those constants quietly goes, while the picture looks exactly as it did. Every panel is now drawn to its own ruler, so a bar that reaches the top of one frame and a bar that reaches the top of the next are the same height and not the same quantity, and the comparison between panels — the only reason to put the panels in one frame — is invented by the layout. The panels are not individually wrong, which is what makes it hard to see: each is a correct chart of its own series, and the ratios inside a panel survive. It is the ratios across panels, the ones the grid is silently offering, that are a fact about the autoscaler. The same rule has a second form, filed under Axis crimes as the auto-ranged axis, where the comparison being broken is not between panels but between one panel and itself at another moment: a grid at least puts the rulers side by side where they can be read against each other, while a single panel that refits itself as its window moves leaves nothing on screen to compare against at all.
1 exhibit in the gallery
The Sankey ribbon
A ribbon is a length that has been bent, and two of them are never added by eye.
A Sankey encodes each quantity as the vertical distance between a ribbon’s two edges, and the arithmetic is usually impeccable — every ribbon to one scale, every node conserving its total. What it asks of the reader is harder than it looks, in three ways. It ranks by shape, so anything split across two ribbons is judged as two ribbons: salary beside benefits, licence beside support, each labelled, each correct, and no shape on the page for the pair. It gives every ribbon a slope, and a sloped band’s width — measured across it, which is the dimension there is to look at — is its drawn thickness times the cosine of that slope, the ink unchanged and the split between width and length quietly moved. And the slope itself is not a fact about the number: it comes from where the band landed in the stacking order and from how much horizontal run the diagram was given, which is a fact about the panel. Under all three sits the plainest thing of all. A Sankey prints no scale, draws no gridline and offers no baseline, so a ribbon can only be judged against its neighbours.
1 exhibit in the gallery
The rainbow colour map
One degree buys seventeen units of colour here and half a unit over there.
A colour ramp is an axis: it converts a quantity into an appearance, and the reader converts it back. Lightness is the one channel with an order everybody already agrees on — hue has none until a convention supplies one — and a rainbow ramp does not spend its lightness in order. Jet climbs from dark blue through cyan to a peak in the yellow, then falls away into dark red, so the brightest thing on the chart is a value from the middle of the range and both ends of the scale arrive drawn dark. The rate is wrong too: equal steps of data buy wildly unequal steps of colour, fast where two hues meet and slow where one hue runs on, so the ramp invents hard edges in smooth data and flattens real gradients elsewhere. None of it shows up in the usual audit, because the scale is linear, the legend is printed, no bin edge was chosen and no value was touched.
1 exhibit in the gallery
The gauge
One number, one needle, and two limits somebody typed in.
A gauge turns one number into an angle, and the angle is set by three things, only one of which is the number. There is no baseline and usually no zero: the needle lands at the value minus the minimum, over the maximum minus the minimum — the minimum shifting every reading and the width dividing it, two settings and neither of them the measurement, both typed in once by whoever installed the thing. Move either and the same measurement moves round the face. On top of that sit the coloured zones, which do something a chart normally leaves to the reader: they convert a continuous quantity into a verdict, at edges drawn long before the data arrived and identical in every context the gauge is ever hung in. And beneath both is the thing a gauge cannot do at all. It has one mark and no time axis, so it can only show a level — where the number is now. Any quantity whose meaning lives in its rate of change is invisible on one, and two moments that mean opposite things arrive as the same picture. That last failure is shared with every single-value display, a big number on a tile included; what a gauge adds is the other two, because it is the snapshot with a scale drawn round it and a verdict printed on the scale.
1 exhibit in the gallery
The radial bar chart
The value sets the angle. The ring sets everything else.
Bend a bar chart into a circle and each bar becomes an arc on its own concentric ring. The value still sets the angle, honestly and exactly — but what the reader measures is not the angle, it is the ink, and the length of an arc is its radius times its angle. So every bar on the chart has been multiplied by its ring, and a ring is not data. It is a slot, handed out by whatever order the rows happened to be in: alphabetical, the order they came back from the query, the order the legend lists them, the sort somebody clicked. Two categories with the same number get different bars; a category with a smaller number gets the longer bar whenever it got the outer ring by enough. The exchange rate is the ratio of the two radii — on a thirteen-ring chart the outermost ring is routinely four or five times the innermost — and it appears nowhere on the page, because the chart has no idea it is applying one. Inside a single ring the arcs are perfectly comparable, which is what makes it hard to see: nothing is exaggerated, no axis is bent, every number is drawn to its own correct angle, and only the comparison between rings — the entire reason the categories were put in one picture — is a fact about the seating plan. Two neighbours share the room and are worth telling apart. “The radar chart” puts categories on spokes from a common centre and asks the reader to judge the area of the polygon they enclose; this one gives every category its own ring and asks for a length that has been multiplied by which ring it got. “The gauge” is the one-ring case with a needle on it. And the coxcomb or polar-area rose is the same family again with the knob turned the other way: there the value sets the radius, so the area grows as the square of it, which is “The area illusion” drawn in polar coordinates. The family resemblance that matters most, though, is to “The free-scale small multiple”: both hand the reader a grid of marks that look like one chart and quietly price a unit of ink differently in each cell, and in both the exchange rate between cells is the one number the picture never prints.
2 exhibits in the gallery
The overplotted scatter
A thousand records in one dot, and one record in one dot.
A scatter plot makes one quiet promise: one mark per record, so more records means more ink. The promise holds right up to the moment two records land in the same place, and after that it breaks without any sign on the page. A second opaque dot on a spot adds nothing, and neither does the thousandth. Where the data is dense, the dots fuse into a solid shape whose size is set by how far the crowd spreads rather than by how many are in it; where the data is sparse, every lonely record gets a whole dot of its own. So a few hundred stragglers scattered across an empty field can cover more of the page than tens of thousands of records packed into one corner, and the eye, which reads covered area as quantity, takes the stragglers for the story. What the chart has really drawn is the range of the data, and it looks exactly like a picture of the distribution. Rounded and whole-number data make it far worse, because then records do not nearly overlap, they tie exactly: when both axes are counts, years or ratings, a thousand identical records are one dot, drawn precisely as large as the single record next to it. Marker size does the rest: a dot wider than the gap between neighbouring values merges records that do not even tie, so the bigger the markers and the tighter the data, the sooner the crowd becomes a slab. Nothing in the audit catches it. The scales are linear and honest, no record has been dropped, every point sits exactly where it belongs, and the only thing missing is the one quantity a scatter plot is usually asked about, which is how many. It is the area illusion running backwards: there, ink grows faster than the value; here, it stops growing at all once a spot is full. And it is a close relative of the heaped digit, since every value people round to is a place where records pile up and vanish into one mark.
1 exhibit in the gallery
The whole-icon pictogram
A row of icons can only count in whole icons.
A pictogram shows a quantity as a count of identical icons: one bucket for every ten gallons, one figure for every million people. It looks more literal than a bar, because you can count the icons. But a whole icon is also the smallest step the chart can draw, so unless someone trims the last icon to size, every value is quietly rounded to the nearest unit before anyone sees it. Each row can then be off by up to half an icon, and nothing on the page says which way, so the gap between two rows can be off by up to a whole icon. Whenever the real gaps are smaller than one icon, the rounding decides the picture: values almost an icon apart can come out identical, values almost level can come out a whole icon apart, and anything smaller than half an icon is drawn as nothing at all. Being countable makes it worse, not better. Readers can count the icons back into a total, and the total is just the rounding added up. Unlike the area illusion, the icons do not change size; the problem is the unit, not the ink. And it is the heaped digit done by the drawing rather than the recording: the values were measured finely and snapped to a lattice on the way to the page.
1 exhibit in the gallery
The acreage choropleth
The data picks the colour. The land decides how much of it you see.
A choropleth fills each region with a colour taken from its value, and then the region’s outline decides how much of that colour reaches the page. The value sets the hue; the acreage sets the ink. Montana gets more than a hundred times Rhode Island’s share of the picture whatever the number says, so a wide, empty region and a small, busy one that land in the same bin weigh very differently in the overall impression. That is harmless when land is what the question is about, and wrong when the quantity lives in tonnes, people or dollars, which do not spread themselves out by the square mile. It gets worse when the colour is a category, such as which product leads or which supplier is biggest, because a category also throws away size: a region that won by a sliver and one that won by a mile wear the same full colour. The reader then judges the country by the share of the map each colour covers, which measures territory, not output. It is a cousin of the area illusion: the eye reads ink, but here the ink comes from geography rather than from anyone’s scaling, which is why it rarely looks like a choice. Unlike the map projection, the map itself can be perfectly equal-area; the land is drawn true, it just is not the thing being counted.
1 exhibit in the gallery
Cherry-picking
The data shown is real. The data missing is the story.
The cherry-picked window
The trend depends on when you press start.
Zoom to the right five years and almost any series can be made to soar, crash, or flatline. The data is untouched — the crop does all the work.
6 exhibits in the gallery
The convenient comparison
We’re #1 — among the competitors we chose.
Any bar looks tall next to the right neighbors. Pick the comparison set after seeing the numbers and “leading the industry” becomes a certainty rather than an achievement.
3 exhibits in the gallery
Survivorship bias
Plotting only the planes that made it home.
If the dataset only contains winners — funds that still exist, companies that went public, planes that returned — every trend tilts rosy. The bullet holes you can see are the ones that didn’t matter.
3 exhibits in the gallery
The ever-rising cumulative
A metric that literally cannot go down.
Plot “cumulative units sold” and the line rises forever, even while the underlying sales collapse. It is the chart equivalent of only counting up.
2 exhibits in the gallery
Regression to the mean
Pick the extremes and they improve without your help.
Almost any measurement is a lasting tendency plus a bit of luck. Sort a group by that measurement and you sort partly on the luck — so the group you picked is more extreme than it really is, and its next reading drifts back toward the average all by itself. Chart the drift and it looks like a treatment working, a trend arriving, or a curse falling.
2 exhibits in the gallery
The self-selected sample
Ten thousand replies, every one of them from somebody who felt like replying.
Some samples are drawn and some samples walk in. When the respondents chose themselves — wrote in, clicked through, left a review, answered the pop-up — what you have is not a slice of the population but a slice of the people moved to reply, and what moves a person to reply is usually the very thing being measured. That makes the bias directional and unbounded, and it means more data cannot fix it: ten thousand volunteers is ten thousand draws from the wrong population. It is the near neighbour of survivorship bias without being the same thing — survivorship is about the cases that dropped out before you looked, self-selection about the ones that stepped forward.
3 exhibits in the gallery
The filter that invents a trade-off
Two things that go together, sliced until they look like a choice.
Some things are worth holding constant and some things are made of the very quantities you are comparing. Price is made of size and quality; getting hired is made of experience and interviewing well; reaching significance is made of sample size and effect size. Slice a dataset by one of those and you have not controlled for anything — you have required the parts to compensate for each other, because the only way into the slice with less of one is more of the other. The two then appear to trade off inside the slice however unrelated, or however positively related, they are outside it. Nothing is exaggerated, nothing is omitted from the chart, and the correlation is computed correctly. The finding is simply about the entry rule rather than about the world.
1 exhibit in the gallery
The late denominator
Start counting at step three and everybody who failed at step two leaves the fraction.
Every rate is a fraction, and a fraction has a top as well as a bottom: somewhere in the process, counting begins. Move that starting line further down the pipeline, past a gate some cases fail to clear, and those cases leave the numerator and the denominator together — so the rate rises without a single outcome improving. Nothing is hidden and nobody is deleted, which is what sets it apart from survivorship bias: survivorship takes the cases out of the dataset, while a late denominator leaves them in it and takes them out only of the fraction, usually a table away, counted and named. They have simply stopped being counted as attempts. The lift is never even, either. It is largest wherever the gate rejects most, which is to say among the cases that were already doing worst, so the same move that raises the headline also flattens the differences the chart was drawn to show.
2 exhibits in the gallery
The size-biased count
A school of forty counts once. So does a school of four thousand.
Every count needs a unit, and a chart of containers gives each container one tally however much it holds. That is the right answer to some questions and the wrong answer to most of the questions people actually ask, because the reader is usually not a school, a class, a bus or a firm — the reader is inside one. Count the contents instead and each container is weighted by its own size, which drags the whole distribution to the right: the big ones, few enough to look like a tail, hold a share of the contents wildly out of proportion to their number. The two averages that result are not rivals and neither is wrong; they differ by exactly the variance divided by the mean, so they agree only when every unit is the same size and diverge fastest where the spread is widest. Nothing is excluded, no axis is bent and the arithmetic is right. The unit is simply not the one the sentence was about.
3 exhibits in the gallery
The reporting threshold
Every row on the chart cleared a line somebody drew. What didn’t clear it isn’t zero — it’s absent.
Most of the best data in the world exists because somebody was obliged to file it, and an obligation has to say who it applies to. So every register carries a line: above this tonnage, this headcount, this turnover, this emissions rate, you report — below it, you do not exist. The line is almost never a judgement about the data. It is a judgement about paperwork, made once, in an impact assessment, by weighing what a return costs the filer against what the regulator gains. Then the register is published, and it is superb: mandatory, audited, comprehensive, unbiased in every respect the word normally means. The trouble starts when it is read as a picture of the world rather than a picture of the filers. Because the threshold is a size rule, what it removes is not a random sample — it is everything small, which is usually most of the units and a minority of the quantity. A line set to capture 90% of the tonnes can easily hold half the objects, and both of those sentences are true of the same rows. Absence then does the rest, because a category with no row does not look like missing data: it looks like a zero, or like nothing worth a row. And thresholds move — a rule is amended, a limit is not indexed and inflation drags units over it — so the same series can step up or down in a year when nothing in the world changed but the eligibility clause.
1 exhibit in the gallery
The immature cohort
Every bar is a whole year. Only the old ones have had time to finish.
Some events do not arrive with the thing they belong to. A recall attaches to a model year built years earlier, a citation to a paper published a decade ago, a claim to the policy year it happened in, a default to the quarter the loan was written, a complaint to the product that shipped last spring. Group those events by the cohort they belong to and the chart looks like a trend, but it is not one measurement repeated: each bar is a count of everything that has arrived so far, and how long “so far” has been running is set by the date somebody pulled the data. The oldest cohort has been collecting for a decade and the newest for a few months, so the x-axis is doing two jobs at once — it is a category axis, and it is a clock running backwards. The damage is always the same shape and always in the same direction. The right-hand end of the chart falls away, the fall gets steeper towards the edge, and the shortfall reads as good news where the events are bad ones: fewer defects, fewer claims, fewer defaults, a safer product, a quieter year. Nothing has been excluded and no axis is bent. The newest bars are simply unfinished, and a bar has no way of saying so.
2 exhibits in the gallery
The file drawer
A chart of the evidence is a chart of the evidence somebody wrote up.
Most of the selection pages in this guide select cases — the planes that came home, the people who felt like replying, the cycles that got as far as a transfer. This one selects findings. The study was run, the analysis was done, the numbers exist; whether they ever enter the record depends on how they came out. That is the whole mechanism, and it is worse than it sounds, because the thing being filtered is the very quantity the chart is measuring. A null is less likely to be written up, less likely to be accepted, and where it is published is likely to lead with whichever outcome did reach significance — which is the same filter running inside a single paper, on one of its own tables. So a literature is not a sample of what was tried. It is a sample weighted by result, and it leans the same way every time: toward the interesting answer. Nothing on the page can give this away. Every study plotted is real, every effect size is correctly computed, the axis starts at zero and the search was exhaustive; the sample frame is the crime, and a sample frame is not a mark on a chart. Pooling makes it worse rather than better, because a meta-analysis is a machine for combining precisely what got published: add studies and the interval tightens around the filtered number, so the picture grows more confident without growing more right. The closest relative in this guide is the reporting threshold, and the difference between them is the useful part. A threshold filters on a characteristic of the unit — a tonnage, a headcount, a turnover — fixed before any data exists, and the rule is published, so a reader who looks can find the line and often an estimate of what sits below it. This filters on the realised result, after the fact, and no rule is written down anywhere: there is no line to look up, no impact assessment to read, and nobody to ask how many studies are missing except a register that may not exist.
1 exhibit in the gallery
The early stop
A test allowed to end whenever it is ahead will end whenever it is ahead.
The other pages in this group choose which rows get drawn. This one chooses when the drawing stops. Run a fair comparison — a trial, an A/B test, a pilot — and the difference between the two arms does not sit still at the truth while the sample grows; it wanders, widely at first and less widely later, and every so often it wanders far enough to look like a finding. A test read once, at a sample size fixed before it opened, raises a false winner 5% of the time when there is nothing there, which is the rate everyone has agreed to live with. A test read every morning and stopped the first time it pleases you is a different instrument entirely, because each morning is another chance for the wander to be extreme, and a rule that stops at the first crossing takes its reading from the upper tail of it. Armitage, McPherson and Rowe put the arithmetic in print in 1969: repeated significance tests on accumulating data raise the probability of a significant result above the nominal level, and it keeps rising with the number of looks. Nothing on the chart records any of this. The counts are real, the interval is the ordinary one, the axes start at zero, and the p-value printed beside the winner is correctly computed for the look it was computed at — it is simply not the quantity the reader thinks it is, because it answers a question about one pre-chosen sample size and the test was given many. The damage comes in two parts. The first is a winner that is not there. The second is that stopping on a threshold selects for a wide gap, so the estimate you keep is biased high — which is why trials stopped early for benefit tend to report larger effects than trials of the same question that ran to the end (Bassler and colleagues, JAMA 303(12):1180–1187, 2010), and why the next study gets powered off a lift that was never available. Its cousin is the cherry-picked window, and the difference matters: a window is chosen inside data that already exists, so a reader can ask for the rest of it. An early stop decides when the data stops arriving, so the rest never exists at all. It is worth holding apart from the two pages about periods that end too soon, as well. The unfinished period and the immature cohort are cut short by the calendar or by the download date — a cut that falls wherever it falls and repairs itself as time passes. This cut is made by the statistic, at the moment the statistic is most flattering, and it never repairs itself, because nobody collects the rest.
1 exhibit in the gallery
The twentieth test
Run enough comparisons on nothing and one of them will come out significant.
A significance test is a promise about one question. Set the bar at p < 0.05 and, when there is truly nothing there, the test will still call a difference one time in twenty. That is the error rate everyone has agreed to live with, and it is a fair price for one question. Ask twenty and the price is paid twenty times. Ask twenty-four, as a dashboard of latency panels or a release review with a metric per region does without anyone deciding to, and when nothing has changed at all the expected haul is a little over one “significant” result, with better-than-even odds of at least one. Then the chart is drawn from the hits. Each bar is real, each p-value is correctly computed for the comparison it belongs to, the axis starts at zero, and the reader is never told that the bars on the page were chosen because they cleared the line out of a larger set that mostly did not. The selection happens before the chart is drawn, which is why the chart looks clean. Correlated metrics change the shape of the problem rather than its size. Metrics computed over the same hosts, patients or customers share whatever luck those units brought with them, so false alarms don’t come more often, they come in clumps: fewer analyses find anything, but the ones that do tend to find several at once, all pointing the same way. Five hits that agree look like five confirmations. They can be one coincidence counted five times. The page has two close cousins in this group, and the difference is what gets multiplied. The early stop takes many looks at one comparison as the sample grows. The file drawer runs many whole studies and publishes the ones that worked. This one runs many comparisons inside a single study, often all at once on the same data, and shows the ones that crossed. All three are the same arithmetic: the more chances a result has to cross the line, the less crossing it means.
2 exhibits in the gallery
The culled denominator
Cut the count and the per-unit figure climbs, even if no unit got any better.
Per-rig, per-store, per-employee and per-acre figures are fractions, and a fraction moves when either half does. When the count underneath is cut hard, two things usually push the ratio up. The first is high-grading: the cut is not random. The weakest stores close first, the least productive staff go first, the rigs that stay drill the best ground, so the average of what is left is higher even if no single unit improved. The second is a lagged numerator: output already in the pipeline keeps arriving after the units that produced it have been counted out (orders booked before the layoff, wells drilled before the rig left), so the top of the fraction holds up while the bottom falls. Either way the chart shows a productivity surge and the reader takes it as a property of each unit, one they can multiply back up when the count recovers. It is not one, and the figure usually falls back as the count returns. It sits next to survivorship bias, which drops the failures from the dataset altogether. Here the failures are counted right up until the cut, and what changes is who is left in the denominator. It is not a late denominator either: nobody is dropped from the fraction by a rule about who counts. The count itself shrinks in the real world, and the ratio is then read as a property of each unit. Nor is it Simpson’s paradox: there is no reversal between pooled and grouped figures, just one ratio compared before and after a cut.
1 exhibit in the gallery
Framing & context
Technically true, practically misleading.
The missing denominator
More of everything happens in California. More people live there.
Raw counts mostly measure population. Big places top every list — sales, crimes, disease — until you divide by the thing the question is actually about.
3 exhibits in the gallery
The shrinking yardstick
Every year is a record year when the dollar does the climbing.
Plot decades of prices in the dollars of their day and the line can only soar — the measuring unit itself loses value every year, so “all-time high” comes free with the passage of time. A long span of nominal dollars is mostly a chart of inflation wearing the data’s clothes.
3 exhibits in the gallery
Spurious correlation
Margarine consumption and the divorce rate in Maine: a love story.
Comb through enough series and some will move together beautifully by pure chance — or because both quietly follow population, inflation, or time itself. A tight fit on a chart is not a mechanism.
2 exhibits in the gallery
Strategic binning
The map whose color breaks were drawn after the data arrived.
A choropleth’s story lives in its color breaks. Set the bins at 0–10, 10–12, and 12–90 and you can paint the country any shade of crisis you like. Continuous data, discrete lies.
2 exhibits in the gallery
Simpson’s paradox
Every group goes one way. The total goes the other.
Break a comparison into groups and each group can point one way while the pooled total points the other, with no arithmetic error anywhere. It happens when the two sides being compared are not made of the same mix of cases: whichever side was handed the easy ones wins the total on case mix alone. The pooled number then mostly records who got which cases, wearing the clothes of a result.
2 exhibits in the gallery
The redefined measure
The step in the line is the year the definition changed.
Long series outlive the rules that made them. A classification is revised, a diagnostic threshold moves, a question is reworded, an instrument gets more sensitive — and the number jumps on the day the change took effect, with nothing in the world having moved. The chart plots both régimes as one line, so the step reads as an event. It is usually disclosed and almost never on the chart.
2 exhibits in the gallery
Relative risk without the baseline
“Raises your risk 18%.” Of what, from what, by how many?
A percentage increase is a ratio, and a ratio means nothing until you know what it multiplied. Eighteen percent more of a one-in-a-million chance and eighteen percent more of a coin flip are the same number on the page and different worlds to live in. Charts drawn in ratio space — axes labelled “% increased risk”, indexes pinned to 100, bars whose height is a change rather than an amount — cannot show the baseline, because the baseline is not on the axis. The reader supplies it from imagination, and imagination runs high.
1 exhibit in the gallery
The missing base rate
Catches four in five. Wrong seven times in ten. Both are true.
Anything that looks for something — a test, an alarm, a screening rule, a model — produces four outcomes, not one: it fires and the thing is there, it fires and it isn’t, it stays quiet and the thing is there, it stays quiet and it isn’t. A detection rate is built from one column of that table, hits over hits plus misses, and it never counts a single false alarm. So it can be pushed to 100% by firing more often, which makes it a threshold setting rather than a score. How much that costs depends on a number the chart almost never carries: how rare the thing being looked for actually is. Hunt something rare and even a good detector’s alarms are mostly wrong, because there is so much more not-it to be wrong about.
1 exhibit in the gallery
The count that measures the looking
The line rose because the instruments did.
Nothing gets counted until somebody notices it, so every count of detected things is two quantities multiplied: how often the thing happened, and how well anyone was looking. Improve the second — more sensors, more screening, a cheaper test, an easier form, a wider mandate — and the series climbs with no help at all from the first, in exactly the shape a real trend would take. It is the near neighbour of the redefined measure and not the same thing: no definition changed here, no threshold moved, no rulebook was rewritten. The same rule was simply applied by more people, in more places, with better equipment, and the growth in coverage arrives on the page wearing the clothes of growth in the world.
2 exhibits in the gallery
The heaped digit
The spike is where the pen stopped, not where the world piled up.
Every number on a chart was written down by something — a person reading a dial, a form with a field on it, an instrument that steps. None of those can express every value, and the ones they favour are not the ones the world favours. Draw the distribution fine enough and what appears is the recording scale rather than the quantity: spikes where a human rounded to a comfortable number, and holes at the values the instrument or the form had no way to record. It is the near neighbour of the count that measures the looking and not the same thing — nothing here is undetected, nothing is missing, and every row in the file is drawn. The values are simply snapped to a lattice somebody chose, and a histogram is fine-grained enough to show you the lattice.
2 exhibits in the gallery
Phantom precision
n = 6, error bars sold separately.
A crisp bar chart looks exactly as confident whether it rests on six million data points or six. Drop the error bars and noise dresses up as signal.
4 exhibits in the gallery
The unfinished period
The last bar is short because the period is young, not because anything changed.
A chart of periods makes a promise so quiet nobody hears it: that each bar is one period, and that the periods are the same length. The last one usually is not. A year drawn at the end of August holds seven months, a month drawn on the third holds two days, and where the figures arrive late even a period that has closed on the calendar is still filling in for weeks afterwards. The bar is drawn at full width regardless, because the width comes from the axis while the height comes from whatever had been counted at the moment somebody pressed download — so the shortfall is a fact about the download date rather than about the world, and it lands in the one position on the chart a reader trusts most, the end, where the story is supposed to be. It is the chart crime with an expiry date. Leave it a few months and it repairs itself, which is exactly why nobody ever goes back to the slide that was already presented. Keep it apart from uneven intervals, which it sits next to: there the unequal bins are known, declared and merely spaced wrongly along the x-axis, so the distortion is in the slope; here the last bin is silently short, nobody has declared anything, and the distortion is in the height.
1 exhibit in the gallery
The date the paperwork arrived
Two dates on every record, and the chart is drawn on the one about the form.
Anything assembled out of reports carries at least two dates: the day the thing happened and the day somebody wrote it down. Only the first is about the world. The second is about a form being filled in — and it is the one almost every system sorts, indexes and charts by, because it is the one the system can be certain of. The event date arrives from a human memory and is sometimes blank; the received date is stamped by the machine, is never missing, and is therefore the default. So the axis quietly stops being time and becomes administrative time, in which nothing happens until it is reported. Every change in how eagerly people report — a broadcast, a lawsuit, a letter from the manufacturer, a new online form, a staff member who chases things up, a hotline number read out on air — lands on the chart as a change in the phenomenon, drawn in the right unit, at the right height, in the right year. Two neighbours sit close enough to be worth holding apart, and the difference in each case is where the damage lands and whether waiting repairs it. The unfinished period also comes from reporting lag, but it bites only the final bin, because that is the one still filling up; wait a quarter and it heals itself. The immature cohort buckets events by the cohort they belong to rather than by a date at all, so its shortfall reaches back years along the whole right-hand end. This one puts the distortion anywhere in the series, usually somewhere in the middle, and it is permanent: a spike drawn on report dates will still be in exactly that year a decade from now, because the records really were filed then. Nothing is incomplete, nothing is provisional, and nothing is waiting to arrive.
1 exhibit in the gallery
The seasonal swing
The biggest move on the chart is the one that happens every year.
Most series that anybody charts have a rhythm inside the year that has nothing to do with how things are going: shops sell in December, plants close in August, exam results arrive in the same week every summer, and a month with an extra Monday in it produces more than a month without one. None of that is noise and none of it is an error — it is a real quantity, correctly measured — but it is the same every year, which means it carries no news, and it is routinely the largest thing in the picture. Draw the raw series and it dominates: the eye finds the biggest movement on the chart and reads it as the story, when the biggest movement is the calendar. The damage is done by the comparison rather than by the line. Set any period against the one immediately before it — this month against last, this quarter against last, a dashboard tile with a green arrow on it — and the answer is mostly the difference between two positions in the year, which is why an industry that shuts for the holidays posts a collapse every August and a boom every September, for ever, in both directions, without anything happening. Two things make it worse than it sounds. The season is often several times bigger than the trend, so a real decline can run underneath a saw-tooth for years without ever being visible. And the fix usually already exists: the same statistical office that published the raw figures published the adjusted ones in the same table, and the chart was drawn from the wrong column.
2 exhibits in the gallery
The extrapolated trend
The data stops. The line does not.
A fitted line is a summary of the points it was fitted to, and of nothing else. Carried past the last observation it stops summarising and starts claiming, about years nobody measured — and it is almost always drawn in the same ink, at the same weight, as the measurements, so the part of the chart that is evidence and the part that is arithmetic arrive looking identical. Three settings decide what that arithmetic says, and charts almost never print any of them: the window that was fitted, the shape that was assumed, and how far the line was carried. Move the window a few years and the slope moves with it; swap a straight line for a curve that fits the same points just as well and the two agree across the data and separate afterwards; extend the horizon and every disagreement grows in proportion. The statistic quoted in its defence measures none of that. R² says how close the fitted points sit to the line drawn through them, it is computed from those points alone, and a series can hand you a tidy fit over any eight years you like while doing something else entirely in the ninth. What ought to be drawn alongside — the uncertainty, widening with distance — usually is not, and where it is, it is generally too narrow, because least squares assumes each year is an independent draw and most real series are nothing of the kind: a wet year follows a wet year, a busy quarter follows a busy quarter, and serial correlation like that makes the honest band wider than the computed one.
1 exhibit in the gallery
The rate at the wrong grain
Ninety-nine per cent per word is eighty-six per cent per sentence.
A rate is a fraction, and the thing in its denominator is a choice. Pick a small enough unit — a word, a character, a packet, a minute, a part — and any error rate becomes a number just under 100%, because the smaller the unit, the less of anything can go wrong inside one of them. But nobody consumes the small unit. A reader reads sentences, a viewer watches programmes, a customer places an order, a patient has a stay, and each of those is made of many small units in a row, every one of which has to come out right. So the rate the reader cares about is the per-word rate compounded across the length of the thing, and that number can be worlds away from the headline while both are computed from the same measurements with no error anywhere. It is not a distortion of the data and it survives every audit of the drawing: the axis can start at zero and run to a hundred, every case can be present, nothing smoothed or dropped, and the picture is still answering a question nobody asked. Two features make it hard to catch. A rate near 100% has almost no room left to move, so real differences arrive as hundredths of a point and read as noise, while the same differences in the complement — the error rate — are whole multiples of each other. And the compounding is exponential, so the gap between the quoted rate and the experienced one widens with the length of the thing, fastest exactly where the stakes are highest.
2 exhibits in the gallery
The establishment label
A row called “clothing stores” counts the stores, not the clothes.
Official business statistics are mostly counted by establishment: each shop, plant or office is given one industry code for its main line of business, and everything it sells, employs or emits is filed under that code. So the row headings in an industry table name kinds of seller, and they read exactly like kinds of product. “Clothing stores” is every sale a clothing store makes, the homeware included, and none of the clothing sold by a department store, a supermarket or a website. A chart that relabels those rows as categories — clothing, furniture, electronics — is answering a question about who did the selling while looking like an answer about what was bought, and the two come apart wherever one kind of seller handles a lot of everyone else’s goods. Online retail is the textbook case. Under NAICS 2017 a web-only retailer is coded as its own industry, so its jeans and sofas never reach the clothing or furniture rows at all, and a table of store types can show every category selling a small share online while the country buys a large share of the same goods that way. Nothing in the figures is wrong; the mistake is in the heading the chart puts over them. (The 2022 revision of NAICS folded most online retailers back into the product-named store industries, which moves the problem rather than ending it: any series that spans the change is now a redefined measure too.)
1 exhibit in the gallery
The gross figure
Counted on the way in. Nobody counted what went back out.
Plenty of quantities have a door at each end: orders come in and get cancelled, customers sign up and leave, goods are sold and come back, jobs are created and lost. Many sources — order books and labour-market statistics among them — report both sides and a net figure besides, and the gross number is often the one quoted first. A chart that takes the gross figure and then asks a net question — is the order book growing, is the customer base bigger, did we keep the sales — has counted every arrival and none of the departures. Nothing on it is wrong. Every bar is the number the source printed, the axis can be impeccable, and the period complete. The error is in what the bar is set against: subtract deliveries from gross orders, or read rising gross sign-ups as a growing customer base, and the outflow that happened in the same year simply never reaches the arithmetic. It does the most damage where the outflow is lumpy, because then the gross series keeps its shape while the net one does not: a year with a wave of cancellations looks like a strong year, the ranking of years can turn over completely, and a stock that shrank is drawn as one that grew. Keep it apart from the missing denominator, which leaves out the size of the thing being counted; here the size is fine, and what is missing is the subtraction.
1 exhibit in the gallery
The mean of a long tail
One billionaire walks into the bar, and the average drinker is a millionaire.
An average is a total divided by a count, and it is only a good stand-in for a typical member when the members are roughly alike. Plenty of quantities are nothing of the kind: incomes, citations, house prices, file sizes, insurance claims, followers, the takings of films and apps. There most items are small, a few are enormous, and the mean is pulled toward the enormous ones — often so far that almost every item sits below it. A chart that plots that mean and labels it “the average X” reads as a statement about a typical X, and it is really a statement about the total, divided evenly among members who did not share it evenly. The trouble grows when the mean is followed over time or compared across groups, because a single new arrival in the tail moves the whole figure: the mean leaps while every ordinary member stays where it was, and the chart draws one item’s fortune as everyone’s. Nothing in the arithmetic is wrong. The error is in the word “average” being read as “typical”, and in a summary that cannot tell the reader whether the number came from many items or one.
1 exhibit in the gallery