This week's materials (Text book Chapter 3 and materials) is more theoretical than practical, but I want your reflection to center around the practical.

Assignment Setup

Grab a deck of standard playing cards. This will be our known population.

Discard the joker.

Give the following cards the listed numerical values

· Aces = 1

· Jacks = 11

· Queens = 12

· Kings = 13

· All numeric cards will take on the same numeric value (e.g., a 5 card = 5)

Ignore the suits (i.e., hearts, spades, etc.).

If we were to graph a frequency histogram for a deck of standard playing cards, it would look something like this:

We get a platykurtic (i.e., flat) distribution because there are four instances of each type of card. Notice the population mean is 7.

Questions

1. What would a distribution of sample means drawn from this “population” of cards look like? Will it approach a normal curve? Will the mean of means be equal to the population mean? (10 points)

2. To see if your answer is correct, draw 25 samples of three cards (replacing the cards and shuffling well after each draw) and calculate the mean rounded to the nearest whole number (e.g., 5.66 = 6). Fill in the draws and means in the table below. (10 points)

3. Create and share a histogram of the means you calculated from the 25 draws. Make sure your histogram has a title. (10 points)

4. Does this histogram resemble the shape of the normal distribution? Is this consistent with the central limit theorem? Why or why not? (10 points)

5. Calculate the mean of means from your 25 draws and write it in the space below. Is it equal to the population mean? (10 points)

Note: This activity was inspired by the demonstration discussed by Matz & Hause (2008) in Teaching of Psychology.

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