Download Distribution of the Sample Mean

Distribution of the Sample Mean
Sampling ‘n’ items from a
population with mean μ
and standard deviation σ
Each sample of ‘n’ items
has a mean
These sample means have
a central tendency and
form a distribution
If ‘n’ is large enough (>30)
the sample means form a
normal distribution.
The Central Limit Theorem
What is the mean of a
group of these samples?
What is the standard
deviation of a group of
these samples?
This distribution has:
mean approximately
equal to the population
mean μ
standard deviation
SD 

n
The Central Limit Theorem
Do different population
distributions change the
result?
A normal distribution is
produced regardless of
the nature of the original
distribution
The Central Limit Theorem
What effect does the
changing the sample size
‘n’ have?
The larger the sample size
the more accurate the
sample mean is.
The distribution of sample
means then has a smaller
standard deviation (there
is less error).
The Central Limit Theorem
What is the standard
error?
SD 

n
is also called the standard
error of the sample
means.
Example
Samples of size 20 are taken from a population of
bats with a mean weight of 90 g and standard
deviation 10 g.
Calculate the mean and s.d. of the means of samples
of bats taken from this population.
E( ) = 90 g
SD ( )