{"id":"central-limit-theorem","domain":"probability-statistics","type":"Theorem","title":"Central Limit Theorem","slug":"central-limit-theorem","url":"/mathematics/probability-statistics/central-limit-theorem/","summary":"Sum/average of many independent random variables tends toward normal distribution regardless of original distribution. Term coined by Pólya, 1920.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Feller, W. (1968/1971). An Introduction to Probability Theory. Vols 1-2, 3rd ed."},{"tier":1,"citation":"Billingsley, P. (1995). Probability and Measure. 3rd ed."},{"tier":2,"citation":"Stigler, S.M. (1986). The History of Statistics. Harvard University Press."},{"tier":3,"citation":"Fischer, H. (2011). A History of the Central Limit Theorem. Springer."}],"relationships":[{"type":"concludes","target":"normal-distribution","label":"Normal Distribution"},{"type":"built_from","target":"random-variable","label":"Random Variable"},{"type":"uses","target":"limit","label":"Limit"},{"type":"uses","target":"series-and-convergence","label":"Series & Convergence"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.8"}