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R0056-28932 · q-20261005-advance-20261006-r07-descriptive-statistics-0007
The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.
G001 — The nonempty observation list is D=[9, 9, 9, -1, -1, -8]. Retain every repetition. Find the arithmetic mean. Give a reduced fraction with positive denominator, retaining /1 for integers.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-mean, observation_mean]
After
derived = [exact_empirical_mean_fraction]
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 = [[9, 9, 9, -1, -1, -8]]
After
derived = [[-8, -1, -1, 9, 9, 9], 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 ALL observations sum := sum(9, 9, 9, -1, -1, -8)
After
Statistics ORIGINAL ALL observations sum = 17
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
Statistics ORIGINAL observation sum over count := div(17, 6)
After
Statistics ORIGINAL observation sum over count = 17/6
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, S003
Before
source roles = [[9, 9, 9, -1, -1, -8], 17, 6]
After
derived = [17/6]
Conditions: none
The mean is the sum of EVERY observation divided by its count.Repetitions each contribute.It may be negative or unattained;reduce with positive denominator and retain/1.
Rule: Statistics_exact_empirical_mean_not_frequency_dedup_mean · Uses: G001, S004
S005 · 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.S004 · premise_and_result_audit — Recompute Statistics ORIGINAL observation sum over count with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL observations sum 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.17/6
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: 4518ab81b5ce16046d3167e787b97887af00a6cc997903deb14c8b52c5bab8edcandidate record SHA-256: fad7ad92c7073e592cab29f24151f5af2466044eb941157b23b4641962f67853semantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED