5.2
The Sampling Distribution of a Sample Mean
Figure 5.8
•averages are less variable than individual observations
•averages are more normal than individual observations
The mean and standard deviation of
x
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= mean of sample, μ
= mean of population
, σ
2
= population variance
select an SRS of size n from a population and measure variable X on each individual in sample
the
n
measurements are values of
n
random variables X
1
, X
2
…
X
n
EX) Randomly select 100 women from the population and calculate their average height.
•X
i
is measurement on one individual selected at random from population→ then X
i
has the
distribution of the population
•if population is large relative to the size of the sample→ X
1
, X
2
…
X
n
considered independent
Mean and standard deviation of a sample mean
Let
x
be the mean of an SRS of size n from a population having mean μ and standard
deviation σ.
The mean and standard deviation of
x
are:
x
μ
= μ
x
σ
=
n
●increasing sample size reduces sampling variability
Sampling distribution of a sample mean
2
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 Spring '11
 Bill
 Central Limit Theorem, Normal Distribution, Standard Deviation, Variance, Probability theory

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