SMALL Function in Apple Numbers: Bottom-N Values and Ties

• Introduced: Documented in Apple’s Formulas and Functions Help 15.4; the original introduction release is not established.
• Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition; it is not a final supported-version endpoint.
• Scope: Shared iWork function help. Availability in individual clients and older releases is not established by this check.
• Checked: October 14, 2026, against the official SMALL reference. Documentation and independent value-selection checks; no native Numbers test.

=SMALL(value-set, ranking)

Both inputs are required. Apple’s SMALL reference permits numbers, dates/times or durations, with all values of the same type. The ranking must be between 1 and the number of values. No omitted-rank default or third direction argument is documented.

Position 1 gives the smallest value. Duplicate values occupy multiple positions, so SMALL is not a lowest-distinct-values extractor. It selects a value; RANK instead assigns a position to a specified member of a collection.

Create a Numbers table named LowMeasurements, with twelve columns A:L and twelve rows including one header row. Put Measurement in D1. Enter these original numeric values in D2:D11; keep the other input columns empty unless using them for labels.

Put Position in F1 and Selected value in G1. Enter integers 1 through 10 in F2:F11. Enter =SMALL($D$2:$D$11,F2) in G2 and fill through G11. The fixed D range preserves the collection as each output asks for a different position.

Do not sort D independently of record labels in a real table. These output values can be inspected without moving any original measurement.

The count-based last-position formula is scoped to this fully numeric ten-entry set. The short SMALL entry does not establish a universal counting shortcut for every supported date or duration type.

In J7 enter =SMALL(D2:D11,4); expect 4. In J8 enter =COUNTIF(D2:D11,"<"&J7); expect 3 observations strictly below the cutoff. In J9 enter =COUNTIF(D2:D11,J7); expect 2 tied at it. In J10 enter =COUNTIF(D2:D11,"<="&J7); expect 5 observations at or below.

Put At most cutoff in L1. Enter =D2<=$J$7 in L2 and fill through L11. Expected booleans are FALSE,TRUE,TRUE,TRUE,TRUE,FALSE,FALSE,FALSE,FALSE,TRUE. Rows 3,4,5,6 and 11 qualify.

If exactly four records are needed, the threshold alone cannot choose between the tied 4s. Apply an explicit tie-breaker based on the purpose of the analysis, rather than removing a duplicate arbitrarily.

To contrast a cutoff without ties, change J7 to =SMALL(D2:D11,3). It becomes 2, with 2 observations below it, 1 equal and 3 at or below. Restore rank 4 after checking. The original measurements and the ten G results are unchanged.

The ascending distinct values are −3,0,2,4,7,10,18. Their fifth value is 7, whereas the fifth observation returned by SMALL is 4. These are different questions.

Create AppleScores separately, with seven columns A:G, four rows and no header rows or header columns. Enter A1:E4 exactly as below; coordinates are labels in the tutorial and are not extra table entries.

Enter =SMALL(A1:E4,1) in G1, rank 2 in G2, rank 5 in G3 and rank 6 in G4. Expected results are 30,51,75,75. Apple’s example explicitly identifies 75 at both fifth and sixth positions. Keep this separate grid distinct from LowMeasurements, whose data have a different minimum and length.

For the ten numeric measurements, rank 0 is below the documented lower bound and rank 11 exceeds the upper bound. If checking those invalid cases, use unused J11 and J12 cells for =SMALL(D2:D11,0) and =SMALL(D2:D11,11). No particular native error token is asserted.

Apple does not separately explain fractional-rank conversion in the cited entry. Use integer positions rather than assuming another spreadsheet’s truncation rule. An empty collection has no valid position under the 1…n bound. Imported text, propagated errors and every mixed-type combination are outside the numeric fixture’s checks.

For noncontiguous collections Apple mentions curly brackets; create specialized references with the formula editor instead of importing unverified array punctuation. Apple’s reference guide explains table-qualified forms such as LowMeasurements::D2:D11. Its function overview explains semicolons between arguments when the decimal separator is a comma.

Use LARGE for highest-first positions, MIN for the minimum alone and COUNTIF to inspect cutoff ties. A function-name match across applications does not prove equivalent date, duration, text or error behavior.