 So let's try and develop a few more measures of center. So let's take a lesson from life. A common practice in life is to use the middle as a compromise position. Suppose we take our set of data values and put them in order. Now remember this only makes sense if we're dealing with ordinal or interval or ratio values. Because those are the only ones where order has any significance. If we do that, we can take the middle value when the values are put in order as a representative. And this suggests the following definition. The median of a set of values is the middle value when the values are put in order. If there are an even number of values, the median will be midway between the two middle values. So for this set of data values, we'll put them in order and the middle value is going to be 6, so the median is 6. For this set of data values, we'll put them in order. This time 6 and 8 are the middle values, and so we'll take the median as midway between the two. The median will be 7. Another way to find a representative value arises as follows. Suppose our data represents a quantity that can be redistributed. So for example, the amount of cereal in a cereal box, if I have a bunch of cereal boxes, I can move some of the cereal from one box to another. Or if I have a number of people investing in a business, the amount of money that each person has invested can be shifted around as people buy each other out. Or if I have a group of people of different heights, I can redistribute the heights of the people, well, no, I can't really make one person shorter by making another person taller and vice versa, so that doesn't really make sense. But in the first two cases at least, it suggests that another possible representative is how much of a fair share of the quantity would be if the quantity were evenly divided. So if everybody puts their money into a business and we want to divide up this money evenly, then this equal distribution amount says something about the data, and so it is another statistic. For example, if the weight of the cereal in five boxes is 15.1 and so on, all in ounces, if the cereal is redistributed so each box contains the same amount, how much is each box going to contain? So we might begin by noting that the total amount of cereal is the sum of the amounts in each box, that'll be 72.2 ounces, and if we distribute this amount evenly among the five boxes, then each box will have 14.44 ounces of cereal. And the idea here is that this 14.44 ounces of cereal represents something about this set of data. In this case, it's the amount of cereal that each box would have if we could distribute the cereal evenly between the five boxes. And so this suggests another useful representative for a set of values, which is known as the mean. The mean of a set of data values is the sum of the data values divided by the number of data values. For example, let's suppose ten students take a quiz and the scores are these. Let's find the mean and interpret its value. So definitions are the whole of mathematics. We'll pull in our definition of the mean. And that says we'll want to add up all of our data values. There are ten data values, so the mean will be this total divided by ten. So what does the mean tell us? Remember, the mean represents the amount that everyone would get if this total amount were distributed evenly. So we might interpret it as follows. If the points on the quizzes could be redistributed, the mean represents the score each student would have if all the students got the same score.