Sampling with Playing Cards

Take a standard deck of 52 playing cards. Shuffle them well. For our purposes, let's assume the Ace is worth 1 point, 2 through 10 are worth their respective points, Jack is worth 11 points, Queen is worth 12 points, and King is worth 13 points. So there are 4 suits with values of 1 through 13 in them. The average value of all cards is 7.00.

Round 1) Deal the cards into 26 pairs. Compute the averages of those 26 pairs. It is possible to get two Aces, in which case the average is 1.00, and it is possible to get two Kings, in which case the average is 13.00. Most likely the averages will tend to be in the 5 to 9 range. Report (1a) the lowest of your 26 averages, (1b) the highest of your 26 averages, (1c) how many of the 26 had an average between 6 and 8 inclusive (within 1 point of 7), and (1d) how many of the 26 had an average of exactly 7.

Round 2) Deal the cards into 13 piles of 4 cards. Compute the 13 averages. Report (2a) the lowest average, (2b) the highest average, (2c) how many of the averages were between 6 and 8 inclusive (within 1 point of 7), and (2d) how many averages were exactly 7.

Round 3) Deal the cards into 4 piles of 13 cards. Compute the 4 averages. Report (3a) the lowest average, (3b) the highest average, (3c) how many of the averages were between 6 and 8 inclusive (within 1 point of 7), and (3d) how many averages were exactly 7.

After each student has posted their results, the instructor will summarize the findings. What we should see is that with samples of size 2, the averages will be spread out greatly, and only a few averages will be close to 7. And with samples of size 4, the spread of the averages will be greatly reduced, with almost every average being between 4 and 10, and most of them close to 7. Samples of size 13 should result in almost every one being close to 7 (although getting exactly 7 is less likely)

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