Cents and the Central Limit Theorem

Project #414 on iSENSEProject.org

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This activity is taken from Activity Based Statistics by Schaeffer, Gnaanadesikan, Watkins, and Witmer

QUESTION

If the shape of a distribution isn't normal, can we make any inferences about the mean of a random sample from the distribution?

OBJECTIVE

In this activity you will discover the central limit theorem by observing the shape, mean and standard deviation of the sampling distribution of the mean for samples taken from a distribution of the mean for samples taken from a distribution that is not normal.

OVERVIEW

In this activity students construct a distribution of the population of the ages of a large number of pennies. They will then construct a histogram of the sampling distribution of the mean of a sample size 10. 

PROCEDURE

 1. Collect 10 pennies

 2. Record the year on our 10 pennies

 3. Find the average year for your sample of 10.

 4. Upload the data to iSENSE. Recording the year and the average.

 Penny Years Distribution

 5. Make a histogram of the years of all the pennies.

 6. Describe the distribution (Shape, Outliers, Center, Spread)

 Sampling Distribution of the Means (n =10)

 7.  Make a histogram of the average year of your sample 

 8. Describe the distribution (Shape, Outliers, Center, Spread)

 

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Name	Units	Type of Data
Penny	year	Number
Average year from your sample of 10 years	year	Number

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Penny	Average year from your sample of 10 years