# Question 28922: Set of All Maximum-Frequency Observed Values [Return to catalogue page 145](https://ocme.evemisslab.com/en/questions/page/145/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261005-advance-20261006-r07-descriptive-statistics-foundations/#q-20261005-advance-20261006-r07-descriptive-statistics-0097) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0056-28922 · q-20261005-advance-20261006-r07-descriptive-statistics-0097 ## Original question and givens The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one. - G001 — The nonempty observation list is D=[24, 24, 24, -1, -1, -23]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one. ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-descriptive-statistics](https://ocme.evemisslab.com/en/mko/mko-descriptive-statistics/) ## Step-by-step derivation S001 · impliesBefore source roles = [qf-statistics-maximal-frequency-set, maximal_frequency_set] After derived = [ALL_frequency_maximizers_numeric_set] Conditions: none Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions. Step identifiers and dependenciesRule: R56_source_answer_role_and_EXACT_family_interface · Uses: G001 S002 · impliesBefore source roles = [[24, 24, 24, -1, -1, -23]] After derived = [[-23, -1, -1, 24, 24, 24], 6] Conditions: none Retain EVERY observation,including repeated values.Numeric sorting changes order only,not n or the sum;do not deduplicate as a set or sort lexically.These are sample summaries,not inferred population laws. Step identifiers and dependenciesRule: Statistics_FULL_observations_MULTIPLICITY_and_numeric_order · Uses: G001, S001 S003 · calculationBefore Statistics ORIGINAL ALL indicators for value-23 := sum(0, 0, 0, 0, 0, 1) After Statistics ORIGINAL ALL indicators for value-23 = 1 Conditions: none Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002 S004 · calculationBefore Statistics ORIGINAL ALL indicators for value-1 := sum(0, 0, 0, 1, 1, 0) After Statistics ORIGINAL ALL indicators for value-1 = 2 Conditions: none Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003 S005 · calculationBefore Statistics ORIGINAL ALL indicators for value24 := sum(1, 1, 1, 0, 0, 0) After Statistics ORIGINAL ALL indicators for value24 = 3 Conditions: none Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S004 S006 · impliesBefore source roles = [[24, 24, 24, -1, -1, -23], all_frequency_maximizers] After derived = [[[-23, 1], [-1, 2], [24, 3]], 3, [24], {24}] Conditions: none Count ALL occurrences in the complete list for each distinct value,and retain EVERY maximum-frequency tie.Under the EXPLICIT all_frequency_maximizers convention,an all-distinct sample returns every value,not another textbook no-mode convention. Step identifiers and dependenciesRule: Statistics_EXPLICIT_ALL_frequency_maximizers_ALL_ties · Uses: G001, S005 ## Reverse checks - S006 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance. - S005 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value24 with exact rational arithmetic, not rounded decimals. - S004 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value-1 with exact rational arithmetic, not rounded decimals. - S003 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value-23 with exact rational arithmetic, not rounded decimals. - S002 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance. - S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance. ## Result {24} The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 63f061e516938251e07a99f16de625f8d771d2a459b74bb341dd294769e370c3 - candidate record SHA-256: 28cf5ef56e388dd7301aaf684237b8cd51edb65e98828ed8aa389d7c0deb8983 - semantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8 - question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759f - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261005-advance-20261006-r07-descriptive-statistics-0097.json)