Assertion: sample's mean | /r/HasProperty | normal
Facets:
value: approximately
type: DEGREE
value: for a large number of samples
type: OTHER
value: in other words
type: DEGREE
value: in shape
type: OTHER
value: with the same
type: OTHER
value: for any population distribution
type: OTHER
value: asymptotically
type: DEGREE
value: regardless of
type: OTHER
value: irrespective of the sample size
type: OTHER
value: always
type: DEGREE
Source sentences:
text: When will the distribution of sample means be approximately normal?
text: To summarize, the distribution of sample means will be approximately normal as long as the sample size is large enough.
text: If the population is normal, then the distribution of sample means will be normal, irrespective of the sample size.
text: In other words, regardless of whether the population distribution is normal, the sampling distribution of the sample mean will always be normal, which is profound!
text: It tells us that, even if a population distribution is non-normal, its sampling distribution of the sample mean will be normal for a large number of samples (at least ??
text: The main implication of the Central Limit Theorem is that for any population distribution, for a sufficiently large sample, the distribution of sample means will be approximately normal.
text: If the sample is small (N < 30), the distribution of sample means will still be normal if the original population was normally distributed.
text: When will the distribution of sample means be approximately normal?
text: It states that a sample mean from an infinite population is approximately normal, or Gaussian, with mean the same as the underlying population, and variance equal to the population variance divided by the sample size.
text: In other words, the sampling distribution of the sample mean will be approximately normal if the sample size is sufficiently large.
text: How many observations are required so that the Central Limit Theorem will assure that the distribution of sample means will be approximately normal?
text: This requirement is necessary to ensure that the distribution of the sample means will be normal even when the underlying data is not normal.
text: Therefore, the sample mean is asymptotically normal: where is a standard normal random variable and denotes convergence in distribution.
text: the distribution of sample means is approximately normal in shape