Limits

What The Median Shape Does And Does Not Mean

The median of the four hundred and five shapes admits one profile in thirty-nine. It is on the front page, and it is the figure most likely to be misquoted.

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Sort the four hundred and five shapes by what they admit and the middle one admits thirteen in five hundred and twelve — one profile in about thirty-nine.

It appears on the front page of this site because it is the most compact summary available of how narrow these filters are. It is also the figure most liable to be turned into something it is not.

For work that changes shape during the week, managers can view the latest official information and review task context rather than a single total. For an independent technical reference, see GitHub.

The median against the two extremes

filled: a requirement that must be met
open: one of the optional ones
area of the inner square: the share admitted
a stroke instead: too small for this panel to draw

Three shapes drawn; one of them admits too little for the square to be drawn, and carries a stroke instead.

The middle row is the median shape of all four hundred and five: five compulsory items, five optional, two of the five needed. Above and below it are the widest and narrowest shapes the record holds.

Computed from the shape of the list. The shape is a stated convention; the count of admitted profiles is arithmetic on subsets.

What it means

Of the four hundred and five list shapes this record enumerates, half are narrower than one in thirty-nine and half are wider.

That is the whole claim. It is a fact about the distribution of shapes in a table.

What it does not mean

It is not a typical list. The record enumerates every shape within its bounds, including many nobody would ever write — a threshold of none, a sixteen-item conjunction. Those count towards the median exactly as much as the plausible shapes do.

It is not a rate. One in thirty-nine profiles is not one in thirty-nine people, for all the reasons the preceding pages give.

It is not a statement about hiring, applications, or anybody's prospects. The record contains no information about any of those and makes no claim about them.

The median of an enumeration is a property of the enumeration. It becomes a property of the world only if the enumeration was a sample of the world, and this one was not.

The figure beside it

One hundred and fifty-two of the four hundred and five shapes admit less than one in a hundred. Thirty-nine of them admit less than one in a thousand.

Those two sit alongside the median on the front page, and they are the damaging pair: the record's own numbers say that a large minority of the shapes it contains are extremely narrow.

They carry the same caveats. They are counts of shapes in a table, not counts of documents in the world.

Why publish the median at all

Because the alternative — publishing no summary — leaves a reader with four hundred and five rows and no way in.

And because the figure does genuine work once the caveats are attached. It establishes that the shapes in this table are narrow, that the narrowness is not confined to a few extreme cases, and that somebody writing a list without computing it will probably land somewhere narrow.

That last implication is the useful one and it is as far as the figure reaches.

A numerical coincidence worth flagging

Thirty-nine appears twice in this record with two different meanings. The median shape admits one profile in thirty-nine; and thirty-nine shapes admit less than one in a thousand.

The two are unrelated. They are not two views of one fact and neither explains the other. They are mentioned together here once, so that a reader meeting them separately elsewhere does not try to connect them.

Where the median sits in the table

It sits low, and the reason is that most of the four hundred and five shapes are narrow.

Sorting all four hundred and five intakes and taking the middle one gives thirteen over five hundred and twelve. Thirty-eight shapes admit half the space or more; one hundred and thirty-two admit between one and ten per cent; one hundred and fifty-two admit less than one per cent.

Band	Shapes
50% or more	38
10% to 50%	83
1% to 10%	132
0.1% to 1%	113
under 0.1%	39

The median lands in the one-to-ten-per-cent band, which holds the largest group. That is a fact about how this record enumerates shapes and not about how often anybody writes them.

Why the mean is not on the front page

Because it is pulled upward by shapes nobody writes.

The mean intake across all four hundred and five shapes is five hundred and eleven over three thousand eight hundred and forty, a little over thirteen per cent — five times the median. The gap comes from the handful of shapes admitting everything or nearly everything, which weigh as much in a mean as any other shape and are rarely the document in front of anybody.

The median is the more honest single figure for a skewed table, which is why it is the one published. Even so it describes the enumeration and not the world, and that caveat belongs with it every time it is quoted.

The form to quote it in

"The median shape in this record admits one profile in thirty-nine, where a profile is one combination of met and unmet items."

The clause at the end is doing the work. Without it the sentence invites the reading this page exists to prevent, and the sentence travels much better than the caveat does.