{ "category": "Statistical functions", "display_name": "FREQUENCY", "entry_kind": "built_in_function", "eval_api": { "method": "POST", "url": "https://handbook.dnacalc.com/api/eval" }, "function_id": "FUNC.FREQUENCY", "implementation_state": { "answer_bank": null, "detail": "Recorded: 7 workbook cells.", "dnacalc_commit": "9e1884369a678158dd82d3d74188daf986995e87", "in_catalogue": true, "state": "matches", "state_label": "Matches every recorded Excel answer", "summary": "Matches all 7 recorded answers", "workbook_corpus": { "cells": 7, "matched": 7 } }, "implementations": [ { "commit": "9e1884369a678158dd82d3d74188daf986995e87", "flavour": "excel-compatibility-candidate", "language": "Rust", "name": "CalcFunc", "own_code": [ "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/statistics.rs#L419-L423", "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/statistics.rs#L519-L534" ], "repository": "https://github.com/DnaCalc/DnaCalc", "shared_code": [ "catalogue/statistics::list" ], "source": "https://github.com/DnaCalc/DnaCalc/blob/9e1884369a678158dd82d3d74188daf986995e87/crates/calc-func/src/catalogue/statistics.rs#L419-L423", "state": "matches", "suite": null, "summary": "Matches all 7 recorded answers" } ], "json_url": "https://handbook.dnacalc.com/api/functions/FUNC.FREQUENCY.json", "name": "FREQUENCY", "notes": [], "schema": "efh.function-reference/v1", "section_order": [ "what-it-does", "try-it", "quirks", "how-to-implement", "version-differences", "alternatives" ], "sections": { "alternatives": "\n### Relationships\n\n- **`COUNTIF` / `COUNTIFS`** — the per-bin alternative. One `COUNTIFS` per interval reproduces\n `FREQUENCY`, and doing so makes the boundary convention explicit instead of implicit, which is\n why it is the usual debugging move when a histogram looks wrong by one.\n- **`COUNTIF` with `\">\"` and `\"<=\"`** — the direct spelling of a single half-open bin.\n- **`MATCH` with match type 1** — the same \"largest boundary not exceeding\" search that a\n sorted-bin implementation performs internally, exposed as a lookup.\n- **`HISTOGRAM` (Analysis ToolPak)** and Excel's chart histogram — separate machinery with its\n own binning rules; agreement with `FREQUENCY` is not to be assumed.\n- **`GROUPBY` / `PIVOTBY`** — the modern aggregation route, which supersedes `FREQUENCY` for\n most reporting uses without superseding it as a function.\n\n\n", "how-to-implement": "\n### Numerical notes\n\n\n`FREQUENCY` has no arithmetic in it, and that makes its numerical behaviour easier to state and\nno less consequential.\n\n**The whole function is a comparison predicate.** Every count depends only on `value ≤ boundary`\nevaluated in IEEE double precision. Two things follow. First, values that a user thinks are\nequal to a boundary may not be: `0.1 + 0.2` is not `0.3`, and a data point produced by\narithmetic lands on the wrong side of a boundary typed as a literal. This is not a defect in\n`FREQUENCY`; it is the boundary convention meeting binary floating point, and it is why bin\nedges chosen midway between achievable data values are the robust choice. Second, the\ncomparison is exact, so the function is *deterministic and reproducible* in a way almost no\nother member of the Statistical category is — there is no summation order, no cancellation, no\ntranscendental.\n\n**Counts are exact.** Integers up to 2⁵³ are exactly representable, and no spreadsheet range\nreaches that, so the returned counts are exact integers with no accumulation error. Any\ndisagreement between two implementations of `FREQUENCY` is therefore a *semantic* disagreement —\nabout the boundary convention, the ignore rule, or the sortedness requirement — never a rounding\none. That is unusual in this category and it makes disagreements here unusually diagnostic.\n\n\n", "quirks": "\n### The bin convention\n\n\nWorth isolating, because it is where readers get the wrong answer while believing they got the\nright one.\n\n| Given bins | Interval for c₁ | for c₂ | … | for c_{m+1} |\n|---|---|---|---|---|\n| b₁, b₂, …, b_m | (−∞, b₁] | (b₁, b₂] | … | (b_m, +∞) |\n\nConsequences:\n\n- A data value equal to b₁ is counted in the **first** bin.\n- A data value equal to b_m is counted in bin m, **not** in the overflow bin.\n- Duplicate boundaries produce an empty interval between them, whose count is necessarily zero.\n- Reversing a \"greater than or equal\" intuition by shifting boundaries down by one unit works\n for integers and fails for continuous data. There is no option to switch the convention.\n\n\n### Result and edge cases\n\n\nReturns `Array` — a vertical array of numbers, of length `LEN(bins_array) + 1`.\n\n- **No admitted values in `data_array`**: documented as an array of zeros. The array still has\n one element more than the bin count.\n- **No admitted values in `bins_array`**: documented as \"the number of elements in data_array\",\n which is the degenerate m = 0 case — a single-element array holding the total count. Note the\n documented wording says *elements of data_array*, while the same page says text and blanks are\n ignored; whether an ignored cell is an \"element\" for this rule is not stated.\n- **Both empty**: falls under both rules at once, which the documentation does not disambiguate.\n- **Duplicate boundaries** give a zero count for the collapsed interval.\n- **The counts are exact integers** held as doubles, so there is no accuracy question about the\n counts themselves. The only comparison performed is `value ≤ boundary`, which is exact IEEE\n comparison — and that is where the numerical content of this function actually lives; see\n **Numerical notes**.\n- **Errors inside the scanned ranges** propagate under the shared coercion discipline; see\n [Coercion and lifting](../model/02-coercion-and-lifting.md).\n\n\n\n### Errors\n\n\nMicrosoft's documentation for this function lists **no error conditions at all**. The Remarks\ndescribe entry mode, the extra element, and the ignore rule; there is no error table.\n\nNeither has a documented counterpart, and neither has been compared against Excel by the\nHandbook. The `#REF!` is the more surprising of the two: `#REF!` is the invalid-reference error,\nand nothing in the documented behaviour of `FREQUENCY` suggests a route to it from\nwell-formed array literals.\n\n\n", "sources": "- Handbook, [The value universe](../model/01-value-universe.md) — array as a value kind and the\n raw-versus-published boundary.\n- Handbook, [Coercion and lifting](../model/02-coercion-and-lifting.md) — scan policy versus\n elementwise lift, and error propagation.\n- Handbook projections `data/functions/FUNC.FREQUENCY.json` (arity, custom coercion and kernel\n classes, reference-visible argument preparation) and `data/presence/FUNC.FREQUENCY.json` (the\n `lookup_prob_frequency_family` module, shared with `LOOKUP`, `PROB` and `MODE.MULT`).\n\n\n", "version-differences": "No comparison between specific Excel builds is recorded here yet. This does not establish that all builds behave alike.", "what-it-does": "\n`FREQUENCY(data_array, bins_array)` counts how many values of `data_array` fall into each\ninterval defined by `bins_array`, and returns those counts as a **vertical array with one more\nelement than `bins_array` has**.\n\nGiven m bin boundaries b₁ ≤ b₂ ≤ … ≤ b_m, the returned counts c₁ … c_{m+1} are\n\n c₁ = #{ v : v ≤ b₁ }\n c_k = #{ v : b_{k−1} < v ≤ b_k } for 2 ≤ k ≤ m\n c_{m+1} = #{ v : v > b_m }\n\nThree properties define the function and all three are documented.\n\n**The intervals are half-open, closed on the right.** A value exactly equal to a boundary falls\ninto the interval *ending* at that boundary, not the one starting there. This is the opposite\nconvention from most histogram tooling — NumPy, R's `hist`, and most plotting libraries default\nto left-closed, right-open bins — and it is the single most common source of off-by-one\ndisagreement when a spreadsheet histogram is reproduced elsewhere. Microsoft's own worked\ndescription is the \"count of test scores in ranges of scores\" framing; the boundary rule\nfollows from the extra-element description quoted below.\n\n**The result has one more element than there are bins.** Microsoft states this directly, and\nexplains the extra element: it \"returns the count of any values above the highest interval\".\nThe m boundaries cut the real line into m + 1 pieces, and the function returns all m + 1\ncounts. Entering `FREQUENCY` over the same number of cells as bins silently discards the\noverflow count.\n\n**The result is a vertical array.** Not a row, not a scalar, whatever the shapes of the\ninputs. Microsoft's wording — \"returns a vertical array of numbers\" — is a shape guarantee, and\nit means an implementation cannot echo the orientation of `bins_array`.\n\nCounts are returned as numbers; the sum of all m + 1 counts equals the number of *admitted*\nvalues in `data_array`, which is not the same as the number of cells in it — see the\nignore rule under **Arguments**.\n\n\n\n### Arguments\n\n| Argument | Meaning |\n|---|---|\n| `data_array` | The values whose frequencies are counted. Documented: if it \"contains no values, FREQUENCY returns an array of zeros.\" |\n| `bins_array` | The interval boundaries. Documented: if it \"contains no values, FREQUENCY returns the number of elements in data_array.\" |\n\n**`FREQUENCY` ignores blank cells and text.** That is Microsoft's sentence, verbatim in\nsubstance, and it is the scan policy for both arguments. Note what it does not say: it says\nnothing about logical values, and nothing about text that looks like a number. Those are\nunsettled here and are on the probe list.\n\nBoth arguments are consumed by scanning. This is not a lift kernel and there is no elementwise\nbroadcast; an array argument is data, not a call to repeat the function.\n\nMicrosoft's remark that `FREQUENCY` \"must be entered as an array formula\" is a pre-dynamic-array\nstatement. On a build with dynamic arrays the result spills from a single cell. The Handbook has\nnot checked how the two entry modes differ on this function, and the difference is exactly the\nkind that changes what a reader sees without changing what the function computes.\n\n\n" }, "signature": { "display": "FREQUENCY(data_array, bins_array)", "parameters": [ { "description": null, "name": "data_array", "optional": false, "repeats": false }, { "description": null, "name": "bins_array", "optional": false, "repeats": false } ], "trailing_repeats": false }, "sources": { "metadata": { "admission": { "label": "implemented", "reason": null }, "arity": { "max": 2, "min": 2 }, "category": "Statistical functions", "classification": { "arg_preparation_profile": "RefsVisibleInAdapter", "coercion_lift_profile": "Custom", "determinism_class": "Deterministic", "error_collapse_profile": "None", "fec_dependency_profile": "RefOnly", "host_interaction_class": "None", "kernel_signature_class": "Custom", "rich_value_usage": "RichBlind", "surface_fec_dependency_profile": "RefOnly", "thread_safety_class": "SafePure", "volatility_class": "NonVolatile" }, "descriptions": { "long": null, "short": "How many values fall into each bin, as a vertical array", "short_source": "dna-calc-own" }, "docs": { "english_description": "Returns a frequency distribution as a vertical array", "microsoft_url": "https://support.microsoft.com/en-us/office/frequency-function-44e3be2b-eca0-42cd-a3f7-fd9ea898fdb9" }, "entry_kind": "built_in_function", "localized_family_names": null, "localized_names": [ { "locale": "ar-SA", "name": "FREQUENCY" }, { "locale": "bg-BG", "name": "FREQUENCY" }, { "locale": "cs-CZ", "name": "ČETNOSTI" }, { "locale": "da-DK", "name": "FREKVENS" }, { "locale": "de-DE", "name": "FREQUENCY" }, { "locale": "el-GR", "name": "FREQUENCY" }, { "locale": "en-AU", "name": "FREQUENCY" }, { "locale": "en-GB", "name": "FREQUENCY" }, { "locale": "en-US", "name": "FREQUENCY" }, { "locale": "es-ES", "name": "FRECUENCIA" }, { "locale": "et-EE", "name": "FREQUENCY" }, { "locale": "fi-FI", "name": "TAAJUUS" }, { "locale": "fr-FR", "name": "FREQUENCE*" }, { "locale": "he-IL", "name": "FREQUENCY" }, { "locale": "hr-HR", "name": "FREQUENCY" }, { "locale": "hu-HU", "name": "GYAKORISÁG" }, { "locale": "id-ID", "name": "FREQUENCY" }, { "locale": "it-IT", "name": "FREQUENCY" }, { "locale": "ja-JP", "name": "FREQUENCY" }, { "locale": "ko-KR", "name": "빈도" }, { "locale": "lt-LT", "name": "FREQUENCY" }, { "locale": "lv-LV", "name": "FREQUENCY" }, { "locale": "nb-NO", "name": "FREKVENS" }, { "locale": "nl-NL", "name": "INTERVAL" }, { "locale": "pl-PL", "name": "CZĘSTOŚĆ" }, { "locale": "pt-BR", "name": "FREQUÊNCIA" }, { "locale": "pt-PT", "name": "FREQUÊNCIA" }, { "locale": "ro-RO", "name": "FREQUENCY" }, { "locale": "ru-RU", "name": "ЧАСТОТА" }, { "locale": "sk-SK", "name": "FREQUENCY" }, { "locale": "sl-SI", "name": "FREQUENCY" }, { "locale": "sr-Latn-RS", "name": "FREKVENCIJA" }, { "locale": "sv-SE", "name": "FREKVENS" }, { "locale": "th-TH", "name": "FREQUENCY" }, { "locale": "tr-TR", "name": "SIKLIK işlevi" }, { "locale": "uk-UA", "name": "FREQUENCY" }, { "locale": "vi-VN", "name": "FREQUENCY" }, { "locale": "zh-CN", "name": "FREQUENCY" }, { "locale": "zh-HK", "name": "FREQUENCY" }, { "locale": "zh-TW", "name": "FREQUENCY" } ], "signature": { "display": "FREQUENCY(data_array, bins_array)", "parameters": [ { "description": null, "name": "data_array", "optional": false, "repeats": false }, { "description": null, "name": "bins_array", "optional": false, "repeats": false } ], "trailing_repeats": false }, "surface_name": "FREQUENCY", "version_marker": null, "xlcall": { "code": "252", "symbol": "xlfFrequency" } }, "microsoft": "https://support.microsoft.com/en-us/office/frequency-function-44e3be2b-eca0-42cd-a3f7-fd9ea898fdb9" }, "try_it": { "formula": "=FREQUENCY({1;2;3;4;5},{2;4})" }, "url": "https://handbook.dnacalc.com/functions/FREQUENCY.html", "variants": [], "versions": [] }