1. MATH 598: Statistics & Modeling for Teachers June 4, 2014

2. Agenda Discussion of Mira Beach
Cents and the Central Limit Theorem Activity
Activity Sheet #2: Exploration of the median

3. Cents and the Central Limit Theorem Activity
We have a collection of ___ pennies. Lets investigate the behavior of the sampling distribution of the mean penny age.
Guiding question:
If the shape of a distribution isn't normal, can the shape of the sampling distribution of the means be predicted?

4. Cents and the Central Limit Theorem Activity
Make a prediction of the shape, mean, and standard deviation of the distribution of the ages of all of the pennies. Explain your reasoning.
What is the shape of the actual distribution? Estimate the mean and standard deviation.

5. Cents and the Central Limit Theorem Activity
What will happen if we increase the sample size? What do you predict about the shape, mean, and standard deviation of a sampling distribution of the means of samples of 10? Samples of 25?
Use software to create a population distribution.
Use software to create approximate sampling distributions of samples of 5, 10, and 25 pennies. Your approximate sampling distributions should include at least 300 samples.

6. Cents and the Central Limit Theorem Activity
Create a graph of the sample size plotted on the horizontal axis and the estimate of the standard deviation plotted on the vertical axis. Use this graph to estimate the equation of the function that best fits the points.
Sample Size, n
Standard Deviation, SD
1 (population) 5 10 25

7. Cents and the Central Limit Theorem Activity
Look at the four distributions that you have created.
What can you say about the shape of the distribution as the sample size, n, increases? About the mean? About the standard deviation?
The characteristic of the shape of sampling distributions is called the Central Limit Theorem. Write a statement of what you think the Central Limit Theorem says. Based on what you observed in this activity, what would you expect your students to say to this question?

8. Cents and the Central Limit Theorem Activity
What did you discover about the relationship between the sample size and the standard deviation of the sampling distribution (standard error)?
Students are likely to see equations involving the mean of the population, the standard deviation of the population, and the sample size (n) in their textbook.
As a result of this activity, what (new) understandings would you expect students to have of the meaning of these equations?

9. Cents Activity
What level of the GAISE Framework do you think this activity is? Why?
How does this activity build on the Text Messages activity?
What extensions might you add to further build your students’ understanding of sampling variability?

10. Activity Sheet #2: Median Exploration
Does the sampling distribution for the median behave in a similar way?

11. For Next Week HW 4: Mira Beach Continued #2 Task
Work individually on the Mira Beach Continued #2 Task.
Keep in mind that your work will be scored and returned to you. So, please write out complete answers. In other words, answer the questions in the manner that you would hope your students would. 