Transcript Measures of Central Tendancy

The Central Limit Theorem
Today, we will learn a very
powerful tool for sampling
probabilities and inferential
statistics:
The Central Limit Theorem
The Central Limit Theorem
If samples of size n>29 are drawn from
a population with mean,  , and
standard deviation,  , then the
sampling distribution of the sampling
means is nearly normal and also has
mean  and a standard deviation
Of 
n
WTHeck?!!!
The Central Limit Theorem
When working with distributions of
samples rather than individuatl data
points we use
rather than 
is called the Standard Error
The Central Limit Theorem
Example
The average fundraiser at BHS raises
a mean of $550 with a standard
deviation of $35. Assume a normal
distribution:
Problem we are used to: What is the
probability the next fundraiser will raise
more than $600?
Sampling problem: What is the
probability the next 10 fundraisers will
average more than $600
The Central Limit Theorem
The average fundraiser at BHS raises
a mean of $550 with a standard
deviation of $35. Assume a normal
distribution:
Problem we are used to: What is the
probability the next fundraiser will raise
more than $600?
The Central Limit Theorem
The average fundraiser at BHS raises
a mean of $550 with a standard
deviation of $35. Assume a normal
distribution:
Sampling problem: What is the
probability the next 30 fundraisers will
average more than $600
The Central Limit Theorem
This makes sense: It would
be much more common for
a single fundraiser to vary
that much from the mean,
but not very likely that you
get ten that average that
high.
The Central Limit Theorem
Example Two:
Mr. Gillam teachers 10,000 students. Their
mean grade is 87.5 and the standard
deviation is 15.
a) What is the probability a group of 35
students has a mean less than 90?