a rule that states that the sampling distribution of means from any population will be normal for large sample n.
(CLT) A fundamental theorem of probability and statistics that states the conditions under which the distribution of a sum of independent random variables is approximated by the normal distribution.
The Law of Large Numbers states that as a sample of independent, identically distributed random numbers approaches infinity, its probability density function approaches the normal distribution. See: Normal Distribution.
This says that as the size of a random sample gets very large, the standardised sample mean of observations of any type of variable will eventually tend to have a normal distribution.
States that the probability histograms of the sample mean and sample sum of n draws with replacement from a box of labeled tickets converge to a normal curve as the sample size n grows
As sample size increases, the distribution approximates a normal distribution and is usually close to normal at a sample size of 30.
states: The means of samples drawn from a population will be distributed normally
From statistics, the theorem that the distribution of sample means taken from a large population approaches a normal, Gaussian, curve.
(CLT) The central limit theorem demonstrates that in large enough samples, the distribution of a sample mean approximates a normal curve, amazingly, regardless of the shape of the distribution from which it is sampled. The larger the value of the sample size (n) the better the approximation to the normal.
A theorem that allows us to us the normal distribution to approximate the sampling distribution whenever the sample is large, even if the distribution of the parent population is non-normal.
All means tend to be normal. For large sample sizes, the sample mean is normally distributed (or approximately normally distributed) irrespective of the distribution of the parent population. The larger the sample, the closer the sample mean to normality.
A mathematically provable principle about obtaining means of samples that has two major ramifications:- The standard deviation of averages of samples from the population will be approximately equal to the standard deviation of the population divided by the square root of the sample size.- Regardless of the shape of the original distribution (even for very non-normal distributions such as exponential distributions), the distributions of averages of samples from the population approach the shape of a normal distribution.
Statistical theorem that explains why many distributions tend to be close to the normal distribution
The central limit theorem | The Fokker-Planck equation
A theorem that states that the distribution of means is approximately normal if the sample size is large enough (n 30), regardless of the underlying distribution of the original measurements.
A theorem that explains why the normal distribution plays such an important role in probability theory.
The theorem that any set of variates with a distribution having a finite mean and variance tends to the normal distribution. This allows statisticians to approximate sets of data with unknown distributions as being normal.
A central limit theorem is any of a set of weak-convergence results in probability theory. They all express the fact that any sum of many independent and identically-distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is called The Central Limit Theorem which states that if the sum of the variables has a finite variance, then it will be approximately normally distributed (i.e. following a normal or Gaussian distribution).
