The first time the kids meet, they have a total of 1+2+3+4+5=$15 between them. The mean is the sum of the data divided by the number of data entries, or 15/5=3. The median of the set is the "middle" value of the ordered set. The median here is also 3...

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The first time the kids meet, they have a total of 1+2+3+4+5=$15 between them. The mean is the sum of the data divided by the number of data entries, or 15/5=3. The median of the set is the "middle" value of the ordered set. The median here is also 3 (2 values below 3 and 2 values above 3).

The next time the kids meet, they have 1+2+3+4+5000=$5010 between them. The mean is `bar(x)=5010/5=1002` , while the median is still 3.

Clearly, the mean has changed significantly, while the median has not changed. (An analogous example is 10 middle income people in a bar; their average wage is $50,000. If Bill Gates walks in, no one originally at the bar makes the "average" as denoted by the mean, but the median will not have moved much.)

Here, the median is a better reflection of how much any one child has. (Select a child at random; 4 of 5 times you will be within $2 of the median, while 4 of 5 times you will be within $1000 of the mean.)

The median is often used with sets that are not symmetric (the same on either side of the "middle") or that have "outliers." (There is no standard definition of an outlier—much like the Supreme Court justice who couldn't define pornography but knew it when he saw it. An outlier is an extreme data point in the set.)

You will often find that home prices in an area are listed with a median; family incomes will be listed as a median; many tests will list a median score, and so on.

Imagine a company. The CEO states that the average wage of her workers is $16.95. An industry periodical lists the average wage at $13.25. A union representative lists the average wage as $10.00. None of the three are lying: the CEO lists the mean (including management wages), the periodical lists the median wage (half above and half below), and the union lists the mode (most common or typical amount) (most are earning the starting wage due to high turnover).