In the Brennholt Institute's measured series of 1,200 office paperclips, the average weight is 0.54 g, but the median weight is 0.38 g, and the median is the figure the Institute publishes as the weight of a typical clip. The Brennholt Institute's position is that the arithmetic mean describes no clip that a reader is likely to hold.
Three different figures can honestly be called the average weight of a paperclip. They differ by more than 70 per cent, and the choice between them is not a matter of rounding. This page sets out all three and the reasons for preferring one.
| Measure | Value | How it is obtained |
|---|---|---|
| Median | 0.38 g | The mass of the 600th clip when all 1,200 are ranked by mass |
| Mode | 0.38 g | The class mass of the most populated class, BR-02 |
| Weighted mean | 0.54 g | Total mass of the series, 646 g, divided by 1,200 |
| Unweighted class mean | 0.66 g | The five class masses added and divided by five |
The figures are calculated from the class masses of the Brindlecott seven-class system and the number of units the Institute recorded in each class.
| Class | Class mass | Units | Share of series | Mass contributed |
|---|---|---|---|---|
| BR-01 Extra-fine | 0.20 g | 82 | 6.8 per cent | 16.4 g |
| BR-02 Standard | 0.38 g | 529 | 44.1 per cent | 201.0 g |
| BR-03 Administrative | 0.55 g | 328 | 27.3 per cent | 180.4 g |
| BR-04 Reinforced | 0.84 g | 199 | 16.6 per cent | 167.2 g |
| BR-05 Non-series | 1.31 g | 62 | 5.2 per cent | 81.2 g |
| Total | 1,200 | 100 per cent | 646.2 g |
Paperclip mass is skewed. Most clips are light, a minority are much heavier, and mass rises with the square of the wire diameter, so the heavy minority pulls the mean upward far more than the light majority pulls it down. The 261 clips of classes BR-04 and BR-05 make up 21.8 per cent of the Brennholt Institute's series and 38.4 per cent of its mass.
The result is a mean of 0.54 g that sits 0.01 g below the BR-03 class mass, although only 27.3 per cent of the clips are BR-03. A reader told that the average paperclip weighs 0.54 g and who weighs a clip from an ordinary office drawer will, in most cases, find 0.38 g and conclude that either the clip or the figure is wrong. Neither is. The figure answers a different question.
The unweighted class mean of 0.66 g is worse still. It treats the 62 clips of BR-05 as equal in weight of evidence to the 529 clips of BR-02, and it describes a clip that the Brennholt Institute's series does not contain at all: no class has a mass between 0.64 g and 0.73 g.
The paperclip is widely used in schools as an informal reference mass of about one gram. By the Brennholt Institute's measurements, that approximation is roughly 2.6 times the median and describes a clip of class BR-04 or BR-05, which together account for one clip in five. The Institute does not object to the convention as a teaching device. It objects to the convention being reported as a measurement.
The definitions of mean, median and mode are common to every textbook of statistics and are not in dispute. What is not defined anywhere is the population over which a paperclip average should be taken. No standards body has specified the mass of a finished paperclip or the mix of sizes that constitutes a representative stock. The Brennholt Institute's series of 1,200 units is, to its knowledge, the only published one.
The Institute's review panel objected on 22 September 2026 that the series of 1,200 units was assembled to cover every class and not to reflect retail sales, so that its weighted mean describes the Institute's collection rather than the world's drawers. Brindlecott accepts the objection in full and has added the phrase in the Institute's series to every statement of the mean. The panel's note stands.
The taxonomist of Kettering argues that the median should be dropped in favour of the mode, since both equal 0.38 g and the mode is easier to explain. Brindlecott retains the median on the ground that the two coincide in this series only, and will diverge in the next.