QUARTILE

What it does

QUARTILE(array, quart)

QUARTILE(array,quart) is the compatibility function for inclusive quartiles. The selector zero means minimum, one lower quartile, two median, three upper quartile, and four maximum.

Try it

=QUARTILE({10,20,30,40},1) returns 17.5, the inclusive 25th percentile. The five selectors give:

Using medians of the lower and upper halves would give different lower and upper quartiles for this example.

Quirks

The selector is truncated to an integer. Empty numeric data or a selector outside zero through four after the current truncation gives #NUM!; a nonnumeric selector gives #VALUE!. Referenced text, logical values and blanks do not extend the numeric sample; zeros and repeated numbers do.

The array need not already be sorted. The selector is a quartile number, not a percentile fraction: pass one for the lower quartile, rather than 0.25. The exclusive quartile convention uses different positions and can reject a requested quartile when the sample is too small.

How to implement

Collect the numeric observations, truncate and validate the selector q, then call the inclusive percentile helper with k=q/4. Sorting and interpolation follow PERCENTILE.

For q=1,n=4, the one-based position is 1+(4-1)/4=1.75; interpolate 10+0.75*(20-10)=17.5. For q=3, the position is 3.25, giving 30+0.25*(40-30)=32.5. Selectors zero and four select endpoints without interpolation. A single numeric observation supplies all five inclusive quartiles.

This definition is a specific percentile convention. Splitting the sample into halves, dropping repeated observations or changing how an odd middle observation joins those halves implements another convention. The current helper’s rank and interpolation arithmetic still need their own numerical controls before a whole-domain Excel claim.

Rust code

17 quartile_legacy "QUARTILE" (2, 2) [R "array", V "quart"] |s, a, sv| { quartile(s, a, sv, false) }

No implementation has been published with a Handbook test suite for this function.

Version differences

No same-input comparison between named Excel builds is recorded for this function here. The documented behaviour below is not a measurement of every Excel release.

Alternatives

QUARTILE.INC names this convention; QUARTILE.EXC uses the exclusive convention; PERCENTILE.INC accepts arbitrary fractions.

Named variants

No named variants are recorded yet.