When beginning statistics, one of the early skills we develop are solving the methods of central tendency.  These are the mean, median, and mode.  They each have advantages and disadvantages and being able to solve for all three is an advantage.  The mean (average) is a quick calculation that doesn’t require sorting a list, so it is often a quick method to be able to describe data.  It’s speed though comes at a cost in that, outliers, either very high or very low, can drastically alter the average in horrible ways.  If you are solving the average house price on a street, and most of the houses are the same, however, there is a massive mansion on the hill, that one mansion will skew the mean 

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The mean is calculated by adding up all of the numbers in a list and then dividing by however many numbers are in that list.  If you wanted a refresher, check out the video below which works through a couple examples.

The median fixes that error in the mean where one or two outliers can horribly skew your data, however it comes at the cost of having to sort the list in order to get your answer.  If your list is small, this is not a huge concern, however with larger lists in order to solve the median you will likely need the support of some spreadsheet software.   There are two situations with median depending on whether the list has an even number of terms, or if there are an odd number of terms.  Each of these are addressed in the videos below before taking on some practice.  Odd is fairly straight forward, even is a little more challenging.

The mode is a little more unique in that there is no equation to solve it.  The mode is the value that repeats the most often.  You are allowed to have a single mode, two or more modes, or if no numbers repeat, you have no mode at all.  Modes are most useful in situations where decimals don’t make any sense to use, the most repeating number is actually valuable.  For example, ordering a popular size of sneakers or restocking a size of coffee cups.  If we worked out the average size coffee cup used and then ordered that, we would have a challenge, beginning with, they likely don’t make it because it would work out to be some decimal sized cup compared to the standard sizes.  In these situations we like the mode.

As a final note, sometimes when we are writing equations for mean we use something called Sigma Notation as a way to quickly define repeat addition, like the type we use for solving the mean.  If you aren’t familiar with Sigma and how it is used in math, please check out the video below.

Looking for additional practice beyond this.  Here are some printable worksheets that can be used to practice these concepts.