If there’s not one value right in the middle, we pick the two closest, then choose the number exactly between them. For our easy example (with data values 11, 12, 13, 13, 14), that first 13 is right in the middle there are two values to the left and two values to the right. In practice, we find the median just like we described in the average height example: by lining up all the data values in order from smallest to largest and picking the value in the middle. Only 13 has no violations, so it’s the median according to the definition. In this section, we’ll explore each of these methods of finding the “average.” All give potentially different results, and all are useful for different reasons. Centrality is just a word that describes the middle of a set of data. They are all methods of measuring centrality (or central tendency). Could we define the average height to be the number that you should guess to give you the smallest possible score?Įach of these three methods of determining the “average” is commonly used. After we check every height and award points accordingly, the person with the lower score wins (because a lower score means that person’s guess was, overall, closer to the actual values). The result is the number of points you earn for that person. You and your friend figure out how far off each of your guesses were from the actual value, then square that number. Once the guesses are made, you bring in every person and measure their height. Imagine a game where you and a friend are trying to guess the typical person’s height. What exactly do we mean when we describe something as "average"? Is the height of an average person the height that more people share than any other? What if we line up every person in the world, in order from shortest to tallest, and find the person right in the middle: Is that person’s height the average? Or maybe it’s something more complicated.
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