Distribution of the sample mean
A population mean, µ, is usually estimated by the mean from a random sample.
If the population standard deviation is σ,
has a distribution with
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= μ |
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= | ![]() |
and is approximately normal if the population is normal or n is reasonably large.
Distribution of the estimation error
Since the error in the estimate is simply the sample mean minus a constant (µ), its distribution has the same shape but is centred on zero,
error = ![]() |
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