Median: When N Is Even

As mentioned in this article, the median of a set of data can be found by continuing to cross out the smallest and largest numbers in the list.

We have found that when n is even, there are 2 terms left at the end that cannot be crossed out. How does one find the median of two terms, then? There's no one individual term that can be the median...

Turns out, in the end, we average the two values to get the median.

When n is even we have no number that falls in exactly the middle of a data set because we cross off all the numbers from the outside in.

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If our data set is {1,2,3,4,5,6,7,8,9,10, 11} when searching for the median we will first eliminate the outermost numbers (1 and 10) then repeat this process until 1 number is left which we call our median (in this case 6).

However is we have an even number of values in our set, we will be left with 2 numbers in the center before all numbers are eliminated. We take the average of these two numbers and call it our median.

For example,

If our data set is {1,2,3,4,5,6} our median is the average of 3 and 4 or $\frac{(3+4)}{2}=\frac{7}{2}$