The average for a set of data corresponds to the equal-shares allocation or fair allocation of the data. For example, suppose that each of 9 people has several dollars and altogether they have $45. The mean of $5 represents the number of dollars each of the 9 people would get if they combined all their money and then redistributed it fairly (i.e., equally).

As seen in Problem A3, the fair allocation of 45 coins into 9 stacks is to place 5 coins in each stack, as follows:

Here is a second allocation of the 45 coins, which is almost fair:

The above allocation is almost fair because most stacks have 5 coins, and the others have close to 5. But, the following allocation of 45 coins doesn't seem fair at all:

Problem B1

Look at these five allocations:

Allocation A

Allocation B

Allocation C

Allocation D

Allocation E

Rank the five allocations on their "fairness," from most fair to least fair. Also, explain how you decided on the level of "unfairness" in an allocation.

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