When a student is taught how to find the mean of a set of data, why might the child have a difficult time accepting the answer?

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Perhaps the most difficult aspect in regards to understanding the mean is that it may be completely "out-of-whack" in regards to the data. In my classes, I usually explain the difference between the mean and the median in the following way... I ask my students how many of them have jobs. Usually a few do and they mainly make minimum wage. So, if we calculate the mean wage of the class it may only be $1 or $2 depending on class size and the number who work. The students usually understand that the mean represents the whole class and no one person actually makes $1 or $2 per hour. Then, I ask them what would happen to the average if a basketball player such as Derrick Rose entered the room. Most of the boys can estimate how much he makes. When we recalculate the mean, we get some astronomical amount for the average. I then ask them if this is what any of them make. They respond "no" and then I explain the concept of an "outlier" and how that can skew the data. Then, we calculate the median and see that it is a more accurate representation of the data if there are outliers.

The mean doesn't have to be one of the data values, for example the mean of {1,2,6} is 3.

The mean doesn't always seem representative of the data. For example, saying that the mean quiz grade for a class with scores of {1,1,1,99,99,99} is 50 is true, but doesn't seem to describe the situation adequately.

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