 This bootcamp takes you through several mathematical concepts and techniques that you need in order to do the introduction to statistics course. Here we are going to learn about a weighted average. Suppose you take three exams but they are not equally weighted. The first exam is worth 20% of the grade, exam two is worth 30% of the course grade and the final is worth 50% of the grade. Your weights are 20, 0.20, 0.30, and 0.50 and now we have one student whose grades were 100, 80, and 90. So how do we compute the average? We set it up in a table so you can see the grade, the weights and you can see the weighted average is now an 89. Notice if you use the symbols it is the sum of the wixi, wixi represents the weights and notice the average again is 89. You'll see it's not the same as a simple average. The table was nice and made things kind of simple but it's not very compact. Using summation notation for the weighted average is actually easier to do. Take a look you have the weights, you have the grades, turns out to be 89 exactly the same as what we had before. Here's a question. What formula would we use if we had all the same weights for the grades? If we were weighing them all the same in order to come up with a course average. Next slide we'll see that. Here we showed that we could use the same formula for a weighted average for the straight average because if we have three exam grades and they all have the same weight, we're talking about one third, one third, one third. It turns out that that average would be 90, not 89 as we had before when the final exam was worth more. We're talking one third, one third, one third as the weights is exactly the same as adding up all the grades and dividing by three. If you can't yet see that it's exactly the same, you should really go back before the course starts and review some of the basic math that you see here. To find more boot camp modules, visit the stat course at the URL you see there and go to the navigation bar on the left, click boot camp and you'll see all kinds of things that are good to do prior to the statistics course. Many of you have already done this before and maybe only need a refresher.