CLT

E31545

probability theory concept statistical theorem

CLT is a fundamental statistical principle stating that the sum or average of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original distribution.

Statements (43)

Predicate	Object
instanceOf	probability theory concept → statistical theorem →
appliesTo	identically distributed random variables → independent random variables → sample means → sums of random variables →
approximationImprovesWith	increasing sample size →
assumes	no single variable dominates the sum →
category	asymptotic result in statistics → limit theorem →
describes	approximate normality of sample means → convergence in distribution of normalized sums of random variables →
enables	approximate normal-based methods for non-normal populations →
field	probability theory → statistics →
formalizes	emergence of normality from aggregation of random effects →
fullName	Central Limit Theorem →
hasVariant	Lindeberg–Feller central limit theorem → Lyapunov central limit theorem → central limit theorem for martingales → multivariate central limit theorem →
historicallyAssociatedWith	Abraham de Moivre → Aleksandr Lyapunov → Carl Friedrich Gauss → Pierre-Simon Laplace →
holdsUnder	appropriate moment conditions → independence or weak dependence conditions →
implies	distribution of standardized sums tends to normal distribution → sample mean is approximately normally distributed for large samples →
mathematicalForm	normalized sum converges in distribution to N(0,1) →
relatedTo	Gaussian distribution → law of large numbers → normal distribution → standardization of random variables →
requires	finite mean → finite variance →
supports	use of z-scores in large-sample inference →
typicalSampleSizeRuleOfThumb	n ≥ 30 for many practical applications →
usedFor	construction of confidence intervals → error analysis in sampling → hypothesis testing → normal approximations to discrete distributions → statistical inference →

Referenced by (2)

Subject (surface form when different)	Predicate
central limit theorem →	alsoKnownAs
CLST →	successorOf