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R0056-28982 · q-20261005-advance-20261006-r07-descriptive-statistics-0057
The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Find the range, defined as maximum minus minimum.
G001 — The nonempty observation list is D=[10, 0, 0, 0, -9, -9]. Retain every repetition. Find the range, defined as maximum minus minimum.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.
Before
source roles = [qf-statistics-observation-range, observation_range]
After
derived = [maximum_minus_minimum]
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.
Rule: R56_source_answer_role_and_EXACT_family_interface · Uses: G001
Before
source roles = [[10, 0, 0, 0, -9, -9]]
After
derived = [[-9, -9, 0, 0, 0, 10], 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.
Rule: Statistics_FULL_observations_MULTIPLICITY_and_numeric_order · Uses: G001, S001
Before
Statistics ORIGINAL maximum minus minimum := sub(10, -9)
After
Statistics ORIGINAL maximum minus minimum = 19
Conditions: none
Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
source roles = [[-9, -9, 0, 0, 0, 10]]
After
derived = [-9, 10, 19]
Conditions: none
The range is max-min and is nonnegative.A singleton or constant sample gives0.Do not substitute original first/last entries for the actual extrema.
Rule: Statistics_range_MAX_minus_MIN_not_ordered_endpoints · Uses: G001, S003
S004 · 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.S003 · premise_and_result_audit — Recompute Statistics ORIGINAL maximum minus minimum 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.19
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 5fa4274c2cd0e1dcafe1cf69de7fe59f403387b69f7e10d8c9d77a4da4cafcf0candidate record SHA-256: 8afbef3706b55058cb61fcea06b97eb52da6c4dba15f1a730d92ca34e93c328csemantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED