Sample mean and sum
The mean of a random
sample, ,
has a distribution that is approximately normal if the sample size, n, is
large and alway has a
mean and standard deviation that depend on the population mean, µ, and standard deviation,
σ,
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= μ |
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= | ![]() |
Occasionally the sum of values in a random sample values is more useful than the mean,
Its distribution is a scaled version of the distribution of the mean — the same shape but different mean and standard deviation.
Mean vs Sum
As the sample size increases,