A distribution chart shows one peak at the tool's default bucket width and three peaks at half that width - which shape is real?

## The chart aggregated before it drew A distribution chart of a single numeric column does not draw your rows. It performs an aggregation first - **the chart's own statistic, computed before any mark exists** - by cutting the value range into buckets of some width, counting how many rows fall into each bucket, and drawing one mark per bucket whose height is that count. Forty thousand rows become perhaps thirty numbers, and everything you read off the picture is a statement about those thirty numbers. Two settings decide what those numbers are: - **the bucket width** - how wide each bucket is, equivalently how many buckets span the data; - **where the buckets start** - the value the first boundary sits on, which pushes every row near a boundary into one side or the other. If you stated neither, the tool chose both with a rule of its own. That is the whole answer to *which shape is real*: **neither shape is a property of the data alone**, because each is a set of counts under a different bucketing, and both sets of counts are correct. ## Why no default can be correct Bucket width trades two errors against each other, and the exchange rate depends on the column in front of you: - **Too wide and distinct groups merge.** Two clusters of values forty units apart fall in one bucket, and the chart shows a single hump that no amount of staring recovers. - **Too narrow and ordinary variation becomes structure.** With a few hundred rows spread across many buckets, each count is small and moves by one or two for no reason worth naming; the eye reads those wobbles as modes. - **Too narrow against the recording precision and you get a comb.** A column rounded to whole units cannot place a value at 3.5, so buckets that can never catch a recorded value sit empty between tall neighbours. That pattern comes from the bucketing meeting the recording, not from the world. Automatic rules exist and every tool applies one, because a chart has to appear. They are heuristics built on assumptions about how many rows there are and roughly what shape the values take. Your column may not satisfy those assumptions, and nothing on the chart will say so. | what you see | what it may be a property of | how to tell | |---|---|---| | one smooth hump | the data, or buckets wide enough to merge groups | halve the width and see whether it splits | | several sharp peaks | the data, or too few rows per bucket | widen the width; count the rows under one peak | | tall and empty buckets alternating | the recording precision against the width | check the distinct values; widen to a multiple of the unit | | a gap in the middle | the data, or where the first boundary landed | shift the start by half a bucket | ## Reading a shape honestly 1. **Redraw at a spread of widths** - at least one clearly wider and one clearly narrower than the tool's pick. A feature that survives them all is robust to the setting, which is worth saying out loud; one that appears at a single width is a property of that width until something else establishes it. 2. **Go to the rows.** Under an interesting peak there are specific records. Count them, and check whether a handful of repeated values, one import batch or one test account produced the whole feature. 3. **Check the recording granularity** before believing any fine structure at all. 4. **State the width on the chart**, in the subtitle or the caption. A shape whose width is unstated cannot be redrawn by a reader and therefore cannot be checked by one. ## What the chart does not tell you - **How many rows it was built from.** You can sum bucket heights by eye only when the vertical axis carries counts; some charts rescale that axis so the total area comes to one, which is another decision the chart made and which erases the sample size completely. - **The individual values.** Every row inside a bucket has become a tally mark. Exact duplicates, ties on a boundary and the single extreme value in the tail all look alike. - **Which rows.** The picture carries no way back to the records, which is why going to the rows is a step and not a flourish. ## The same trap under another name Replace the buckets with a smooth curve fitted over the values and the problem has not gone away - it has been renamed. Each part of such a curve averages over a neighbourhood of nearby values, and the width of that neighbourhood is exactly as unchosen as the bucket width was: wide erases structure, narrow invents it. The curve is also more persuasive than a row of bars, because smoothness reads as a finding rather than as a setting. Ask it the same two questions: who chose the width, and does the feature survive another one?