What can be asked

Three Questions, Or A Hundred Thousand

The narrowest board permits three questions; the widest permits one hundred and seventeen thousand six hundred and forty-nine.

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A board with one filter of two choices permits three questions: one value, the other value, or neither set.

A board with six filters of six choices permits one hundred and seventeen thousand six hundred and forty-nine.

If a team already has strong project data, it can still explore the workforce toolkit and compare the setup without committing to deployment. For a separate technical reference, see Tableau.

The median across the four hundred and sixty-one schemas is three thousand six hundred.

What boards allow

the upright: where this figure falls on the record's range
the ticks are powers of ten; the scale is logarithmic

Three figures placed; the range is the record's own, over queries.

The full range of what a schema permits, logarithmically. Three questions at one end and six figures at the other.

Placed on the full range the record holds. The scale is the record's own, and the drawing refuses a scale that is not.

Reading the median honestly

Two schemas reach exactly three thousand six hundred questions: five filters of three, four, four, five and five choices, and six filters of two, two, three, three, four and four.

Their cell counts are one thousand two hundred and five hundred and seventy-six. So even at the median of one figure, the other figure is not pinned down — the two schemas sitting there differ by more than a factor of two in resolution.

This is the trap worth marking before going further. The median question count and the median cell count do not belong to the same schema. Not approximately, not nearly: no schema in the record has both eight hundred and sixty-four cells and three thousand six hundred questions. The schemas with eight hundred and sixty-four cells permit between one thousand seven hundred and fifteen and five thousand two hundred and ninety-two questions.

"The median schema" means nothing until somebody says median of what. Two medians, two different schemas, and the phrase hides it.

The distribution

Questions	Schemas
fewest, 3	one
median, 3600	two
most, 117649	one

Both ends are unique, as both ends of the cell range are: there is one way to build the smallest schema and one way to build the largest.

Between them the figures are dense. Four hundred and five distinct question counts occur across four hundred and sixty-one schemas, which is a collision rate far lower than the cell counts manage: one hundred and ninety-five distinct cell counts across the same four hundred and sixty-one.

Why question counts spread out more

Because the factors involved are larger and include primes the cell counts never see.

Cell counts are products of two, three, four, five and six. Question counts are products of three, four, five, six and seven. The seven is decisive: it is prime, it is larger than anything in the cell range, and a product containing one cannot be rebuilt from factors that do not.

So every schema containing a facet of six values carries a seven in its question count, and that seven marks it. Schemas without a facet of six cannot reach the same figures at all.

The result is that the largest group of schemas sharing a question count holds three, where the largest group sharing a cell count holds seven. The second figure is simply a sharper instrument.

What the range means in practice

A reader moving between two boards may be moving between three available questions and several thousand, with nothing on either page announcing it.

The visible signals are weak. A long sidebar suggests many questions and often delivers them, but the class of seven shows six filters and three filters producing identical resolution, and a reader counting controls learns about neither figure reliably.

The figure is cheap to get and nobody gets it, which is the recurring shape of this whole record: the informative property is one minute of arithmetic away, and the property everybody uses instead is the one visible at a glance.

Why both ends are unique

There is one way to build the smallest schema and one way to build the largest, so each extreme is reached by exactly one structure.

That sounds trivial and it has a consequence worth noting: the two schemas at the ends of the question range are the only two in the record identified by their question count alone with no ambiguity whatsoever, and they sit where nobody looks.

Everything in between has company. Four hundred and five distinct question counts across four hundred and sixty-one schemas means fifty-six schemas are sharing, in groups of two and three.

The one caution on this figure

A large question count is not a promise that the questions are useful.

The page on one-choice filters shows how to double a question count while adding nothing: a filter with a single option contributes a factor of two to this figure and a factor of one to the resolution. Every question it adds is a duplicate of a question already there.

So the question count is only trustworthy alongside the cell count, which is the same conclusion the record keeps arriving at from different directions. One figure classifies; two identify; and each of them, alone, can be inflated by something the other would expose.