Download Sample mean: M. Population mean: μ. μ is pronounced `mew,` like

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Transcript
Sample mean: M.
Population mean: . ispronounced ‘mew,’ like the sound a kitten makes.
We used ‘m’ with the symbol font to get .
We introduced the concept of a sampling distribution, which is the distribution a
statistic will take when calculated from multiple independent samples. One
particularly important (or central) sampling distribution is the distribution of the
mean across very many, or even all possible, samples of a particular size. The
central limit theorem tells us the properties of that sampling distribution.
The Central Limit Theorem
Part One:
The mean of all possible sample means will equal the population mean.
(‘All possible’ is roughly the same as ‘a very large number’.)
The standard deviation of those sample means will equal the population
standard deviation divided by the square root of the sample size.
Part Two:
If the population is normally distributed, then the distribution of sample
means will also be normally distributed.
If the population is not normally distributed, but is not so horrible that it
doesn’t have a mean or has infinite variability, then the distribution of
sample means will become normal as the sample size becomes large. (How
large is ‘large’ is a question for which the answer is ‘it depends.’ For some
non-normal distributions, sample size as small as 10 might be sufficient,
and for others, 200 might not be a large enough sample size.)
To avoid confusion, the standard deviation of a sampling distribution is
known as the standard error. So we would refer to the standard deviation
of the sampling distribution of the mean as ‘the standard error of the
mean.’