Two tools draw a box mark for the same column and show different points beyond the whiskers - why?
answer
- the box shows no rows
- whisker ends come from a rule
- the rule differs between tools
- state the convention, then compare
basics
~20 sThe whisker rule is a convention the chart chose, not a fact about the data: a multiple of the middle-half spread, a fixed percentile pair, or the extreme values. Different conventions, different points drawn beyond them.
solid answer
~50 sA box mark is entirely a pre-draw statistic - the box edges, the line inside it and the whisker ends are all positions computed from the sorted values, and the rows themselves are gone by the time anything is drawn. The whisker ends in particular come from a convention, and the conventions in circulation disagree: extend to the furthest value within a multiple of the middle-half spread and draw everything past it individually; stop at a fixed pair of percentile positions; or run to the extremes, in which case nothing is ever drawn beyond. Each is a setting, and none is the rule. So a point drawn separately means *beyond the whisker under this chart's convention*, not *an anomaly the data identified*. Never compare whisker extents across two charts without checking that both used the same rule, and state the rule you used.
go deeper
Know that a box mark draws computed positions, not records, and that the whisker ends come from a rule the chart applied. Being able to say the rule is a setting is enough at this level.
Name the rival conventions and what each implies: a multiple of the middle-half spread, a fixed percentile pair, the extremes. Explain why two tools can draw different points beyond the whiskers from one column and both be right.
Show that you check the convention before any comparison, put the rule and the row count on the chart, and refuse to let a whisker end become a threshold. Treat a separately drawn point as something to look up, not as a verdict.
Decide whether your team fixes one whisker convention across its reporting and pays the cost of enforcing it, or accepts per-tool defaults and requires the rule in the caption. Undocumented defaults quietly become policy when someone reads a limit off a chart.
## Everything in a box mark was computed before drawing A box mark shows no rows. Its edges, the line inside it and the ends of its whiskers are all positions the chart computed from the sorted values of the column, and the records themselves never reach the page. That makes the mark an extremely dense summary - a few hundred thousand values in a shape two centimetres wide - and it makes every part of the shape a consequence of a rule rather than an observation. Most of those rules are stable across tools. **The whisker rule is not**, and it is the part readers treat as a finding. ## The conventions in circulation, and what each one implies | convention | where the whisker stops | what gets drawn beyond it | |---|---|---| | a multiple of the middle-half spread | at the furthest value still inside that distance from the box | every value past it, drawn as its own mark | | a fixed pair of percentile positions | at those positions, wherever the values happen to fall | with enough rows, a roughly fixed share of the values every time | | the extreme values | at the smallest and largest value present | nothing at all, by construction | | a variant with a notch or a different multiple | wherever that variant's parameter puts it | more or fewer marks, with the same appearance | Every one of these is configurable in the tools that offer it, and the multiple itself is a parameter. So two charts of **the same column** can show different whisker lengths and different sets of separately drawn points, and neither chart is wrong. They answered different questions that look identical on the page. ## Why this bites in practice The damage is rarely aesthetic: - **Two reports disagree** about how many anomalous orders a region had last month, and the disagreement is entirely between two tools' defaults. Hours go into the data before anyone checks the marks. - **A threshold gets read off a whisker.** Somebody sets an alerting limit at the end of a whisker on last quarter's chart. That position depends both on the convention and on the rows in that particular sample, so it moves when either changes - and nothing recorded which convention produced it. - **A point drawn separately gets called an outlier**, which imports a claim the chart never made. What the chart said is *this value sits beyond where this rule put the whisker*. Whether it is an error, a rare but genuine event, or an ordinary value in a long-tailed column is not something the mark can tell you. ## What the box hides even when the rule is stated - **How many rows it summarises.** A box built from thirty values and one built from three million look the same, so a side-by-side comparison silently compares two very different weights of evidence. - **The shape between the edges.** A column with two well-separated clusters and one spread evenly across the same range can produce nearly the same box; the summary keeps positions and discards structure. - **Ties and duplicates.** Repeated values collapse into the same position, so a mark drawn beyond a whisker may be one record or four hundred identical ones. ## What to do about it 1. **State the rule on the chart** - in the caption, as plainly as the axis label. It costs one line and makes the mark reproducible. 2. **Fix one rule for any comparison.** Before two charts are placed side by side, or one is compared with last quarter's, confirm both used the same convention; redraw rather than argue. 3. **Show the row count per box**, so a box over a handful of records cannot be read against one over millions. 4. **Call a separately drawn point what it is** - a value beyond the whisker under this rule - and go to the record before calling it anything stronger. 5. **Reach past the box when the shape matters.** If the question is whether the column has two clusters, a summary that keeps only a few positions is the wrong mark for it. The general habit is the one this whole surface rewards: when a mark draws something you did not compute, find out which rule computed it, and put that rule where the reader can see it.
- Under a percentile-pair whisker convention, why is there usually something drawn beyond the whiskers?Because the rule reserves a share of the values by construction rather than reacting to the shape: the whisker stops at a fixed position in the sorted values, so with enough rows there is always a tail past it. Those marks are the ordinary extremes of the column, not candidates for investigation.
- An alerting threshold was set at the end of a whisker on last quarter's chart - what is wrong with that?The whisker end is a function of the convention and of the rows in that one sample, so it moves when either changes, and the convention was probably never recorded. A threshold should come from a stated rule applied to stated data, not read off a mark whose rule is unknown.
saying these in an interview costs you the question
- Calls every point past a whisker an outlier the data identified.
- Assumes all tools extend whiskers to the same multiple of the middle-half spread.
- Compares two charts' whisker lengths without checking either convention.
- Thinks the box shows rows rather than a few computed positions.
- Reads two similar boxes as two similar distributions.