Name_________________________________
ADVANCED PROBABILITY AND STATISTICS
SAMPLING DISTRIBUTION OF X BAR
THE BACKGROUND
As you recall from the notes, to construct a sampling distribution of x-bar, you must gather all the
possible combination of samples of size n and find the sample mean of each. So, essentially you have
this large collection of sample means (x bars). You can then create a graph of this sampling distribution.
When you graph the population, you are graphing all of the individual observations. When you graph a
sampling distribution, you are not graphing individual observations. You are graphing means of sample
of size n. We want find out how the shape, center, and spread of this sampling distribution changes in
relation to the original population as the sample sizes get larger.
THE ACTIVITY
I have collected all of the UK Men’s Basketball scoring performances through last season (you will be
given a copy of this Excel document). Below you will find the graph of this distribution. This is our
population.
350
300
Frequency
250
200
150
100
50
0
24-33
34-43
44-53
54-63
64-73
74-83
84-93 94-103 104-113114-123124-133
UK Offensive Output
Center:
µ (the mean of our population) = 76.93
Spread:
σ (the standard deviation of our population) = 13.9
Shape: ________________________________________________________
Remember we are going to be constructing multiple sampling distributions from this population of
different sample sizes. We will compare each of these sampling distributions to our original population
distribution graphed above.
SAMPLING DISTRIBUTIONS (with a partner)
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Choose a partner to work with.
Each set of partners needs graphing calculators and one set of UK Men’s Basketball scoring data.
One partner will be the calculator operator and one partner will be the sampler.
For each sample size one partner will use the randint function on the calculator to choose the
appropriate number of games. If the sample size is 10 you will choose 10 different games.
The second partner will use the Excel Document to locate the games.
The partner with the calculator will then find the mean of the sample.
You will repeat this process 10 times and then combine this data with the rest of the class to
create a sampling distribution.
SAMPLE PART 1
Sample 1
X bar
(n = 10)
2
3
4
5
Now with the combined data from the class, draw a rough sketch of the sampling distribution. Make
sure you label your graph.
Center:
µ x̄ =________
Spread:
σ x̄ =________
Shape: ________________________________________________________
How do the center shape and spread of this sampling distribution compare to the original population
distribution?___________________________________________________________________________
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SAMPLE PART 2
Sample 1
X bar
(n = 20)
2
3
4
5
Now with the combined data from the class, draw a rough sketch of the sampling distribution. Make
sure you label your graph.
Center:
µ x̄ =________
Spread:
σ x̄ =________
Shape: ________________________________________________________
How do the center shape and spread of this sampling distribution compare to the original population
distribution?___________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
SAMPLE PART 3
Sample 1
X bar
(n = 30)
2
3
4
5
Now with the combined data from the class, draw a rough sketch of the sampling distribution. Make
sure you label your graph.
Center:
µ x̄ =________
Spread:
σ x̄ =________
Shape: ________________________________________________________
How do the center shape and spread of this sampling distribution compare to the original population
distribution?
_____________________________________________________________________________________
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ANALYSIS (individual)
Now that you have gone through the effort with the help of your classmates to construct three different
sampling distributions of sizes 10, 20, and 30, I want you to answer the following questions in complete
sentences:
1) How does the shape of the sampling distribution change compared to the population as your
sample size increases?
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2) How does the center of the sampling distribution change compared to the population as your
sample size increases?
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3) How does the spread of the sampling distribution change compared to the population as your
sample size increases?
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