Math215 Statistical Concepts: Generating a Sampling Distribution of Sample Means
An assignment exploring statistical sampling distributions.
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Math215 Statistical Concepts Name: ________________________
1
081215
Generating a Sampling Distribution of Sample Means
In this assignment we’ll illustrate the idea of a sampling distribution in the case of a very small
sample from a very small population.
The population will be the ages of six people from your family or friends. The parameter of
interest will be the mean age, μ, of this population. First, identify the six people in your family
or friend groups and record their ages. Then follow the steps below to generate a sampling
distribution and answer the questions.
1. Record the data of your population in the table below. (i.e. the ages of the 6 people in your
family or friends. Population size is N=6)
Individual 1 2 3 4 5 6
Age 25 23 18 16 27 30
2. Find the mean age, μ, and the standard deviation, σ, of this population.
μ = _23.16_____________
σ = _5.34_____________
3. Now, take 10 different random samples of size n= 3 from this population. You can use your
calculator (See the instructions in Appendix A at the end of this assignment document) OR use
Excel (See the YouTube link in Appendix B) to generate 10 random samples of size 3. Calculate
the mean of each sample. List the ages in each sample and their mean in the table below:
Sample Items Sample means, 𝑥̅
1. 16,23,18 𝑥̅ 1 =19.00
2. 27,25,23 𝑥̅ 2 =25.00
3. 23,30,18 𝑥̅ 3 =23.67
4. 16,27,18 𝑥̅ 4 =20.33
5. 18,30,16 𝑥̅ 5 =21.33
6. 23,18,27 𝑥̅ 6 =22.67
7. 18,16,23 𝑥̅ 7 =19.00
8. 30,25,27 𝑥̅ 8 =27.33
9. 18,16,25 𝑥̅ 9 =19.67
10. 30,27,23 𝑥̅ 10 =26.67
4. Without actually calculating
i. Predict what the mean of 10 sample means from your table above should be: ___23_____
ii. Predict what the standard deviation of 10 sample means from your table should be: _5_____
1
081215
Generating a Sampling Distribution of Sample Means
In this assignment we’ll illustrate the idea of a sampling distribution in the case of a very small
sample from a very small population.
The population will be the ages of six people from your family or friends. The parameter of
interest will be the mean age, μ, of this population. First, identify the six people in your family
or friend groups and record their ages. Then follow the steps below to generate a sampling
distribution and answer the questions.
1. Record the data of your population in the table below. (i.e. the ages of the 6 people in your
family or friends. Population size is N=6)
Individual 1 2 3 4 5 6
Age 25 23 18 16 27 30
2. Find the mean age, μ, and the standard deviation, σ, of this population.
μ = _23.16_____________
σ = _5.34_____________
3. Now, take 10 different random samples of size n= 3 from this population. You can use your
calculator (See the instructions in Appendix A at the end of this assignment document) OR use
Excel (See the YouTube link in Appendix B) to generate 10 random samples of size 3. Calculate
the mean of each sample. List the ages in each sample and their mean in the table below:
Sample Items Sample means, 𝑥̅
1. 16,23,18 𝑥̅ 1 =19.00
2. 27,25,23 𝑥̅ 2 =25.00
3. 23,30,18 𝑥̅ 3 =23.67
4. 16,27,18 𝑥̅ 4 =20.33
5. 18,30,16 𝑥̅ 5 =21.33
6. 23,18,27 𝑥̅ 6 =22.67
7. 18,16,23 𝑥̅ 7 =19.00
8. 30,25,27 𝑥̅ 8 =27.33
9. 18,16,25 𝑥̅ 9 =19.67
10. 30,27,23 𝑥̅ 10 =26.67
4. Without actually calculating
i. Predict what the mean of 10 sample means from your table above should be: ___23_____
ii. Predict what the standard deviation of 10 sample means from your table should be: _5_____
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University
National University
Subject
Mathematics