I've heard some lower math abused in some interesting ways regarding reality and decided that a combination primer and reference is needed. This is it.
The median, like the mean and mode, is a measure of central tendency. If one takes a group of numbers and lists them in numerical order, the median is the mid point. (The mean is the traditional average, which is the total of the values divided by the number of items. The mode is the most frequently occurring. Where there is no such animal, there is no mode.) For any number of elements "n", the median is (n+1)/2 from either end. For 9 items, for example, it is the (9+1)/2 = 10/2 = 5th item. Now, just for grins, I'll make some lists --
9 50 103 8 40 102 7 30 101 6 6 100 5 5 5 This row is the median 4 4 1 3 3 1 2 2 1 1 1 1
5 15.67 46.11 This row is the average Only the 3rd column has a mode. The mode is 1.
Now, what does the median, in and of itself tell us? Pretty much zip shit.
Let's say those are incomes in Sam's Sweatshop's in different locales. The only information we get from knowing that the median is 5 is that half of the folks make greater than or equal to 5 and half of them make less than or equal to 5. From this we can further conclude that the sub-population earning more earns more in the aggregate than the sub-population earning less, but, duh. So when people start arguing from the median income, raise your trouser legs a bit, because there is pretty much no useful information conveyed by its specific magnitude.
Now. let's say these are election results in different locales and, in each, a candidate named Josephine Smith won the median number of votes. What does that signify? As above, pretty much zip shit. Does it mean that she is therefore a centrist? Hell no. (ignoring the separate issue that there is really no such thing and the term is bogus) Does it define the center and hence centrism and centrists? That is absolutely preposterous. Again, when people start spouting off about the median, raise your trouser legs, or, in the case of elections, put on hipboots.
For what it is worth, children are taught that the mean, median, mode and range are all needed to get any understanding out of this kind of data. Statisticians throw in the standard deviation. That provides more information and clarifies things some, but in many cases answers no questions in some arena because the data doesn’t address the questions. “What is the median earthly altitude above sea level” tells us nothing about the political beliefs of Dianne Feinstein, for example.