 This bootcamp takes you through several mathematical concepts and techniques that you need in order to do the Introduction to Statistics course. One of the things you might worry about in looking ahead to your statistics course is a plugging numbers into a formula and calculating the result. Is it going to be different if you do the intermediate calculations in the wrong order? You're right to be worried about it because actually it will. And if you do the calculations in the wrong order, you're going to get the wrong answer. And very often you're not going to be able to get credit for your work. Very important to know what you're doing. If you have a large complicated formula, what do you do? Well, if you see parentheses, that comes first. After that, if you have exponents like x squared, that goes next. If you have square roots, that's at that level. And after that, multiplication and division, after that addition and subtraction. Inside of any level, it doesn't matter what goes first and second and third. But you really have to be careful of the order, especially parentheses. The example at the top here is a very, very simple example of what we're talking about with order of operations. We know if we take an average, we want to add all the numbers up first and then divide by 3 if we have 3 numbers. So in this case, 10 plus 3 plus 17 divided by 3 comes out to 10. 30 over 3 is 10. We know we want to do all the numbers to add up all the numbers in the numerator first because we know we have to do the parentheses first. In the second example, we have z equals, and by the way, you're going to come back to that z over and over again. Once we start the statistics course and have it and get it rolling. But in this particular example, z is equal to 120 minus 110 on the numerator. And imagine there's parentheses around that because it's in the numerator, it's going to be done first. And then in the denominator, we have a bunch of stuff, two fractions under a square root, and each of the fractions has a square in the numerator. That's kind of complicated. How are we going to do that? Well, first we have to say, okay, the numerator gets done first. Imagine it was in parentheses, 120 minus 110 gives you 10. And then in the denominator, we have 10 squared over 100. That's the first fraction. The 10 squared gets done first. We take that 10 squared, which is 100, divide by 100. That gives us one. The other fraction, we still didn't do the square root because we have to do the other fraction first. We have to do with everything under the square root first. 20 squared, we do the 20 squared, and we divide that by 80. We end up with a 5. Finally, 1 plus 5 is 6. We put that under the square root. Now we can do the square root. The square root of 6 is 2.45. Now we can finally do the original fraction, z equals 10 over 2.45, and it's equal to 4.08. So here's an example of how we do this. The first example at the top is just a simple average of 3 numbers, 10 plus 3 plus 27. Add that up, divide by 3. You get 30 over 3 or 10. Here's another example just to give you more practice. If you need more practice, I'm sure you can find examples in your high school algebra book. T is equal to 200 minus 180, so the numerator is 20. Now the denominator has a square root. It has 400 multiplied by then something inside of parentheses. And inside of parentheses, what do we have? Two fractions that we have to add up. That gets done first. If you get 0.15 multiplied by 400, put that under a square root, then you can finally take 20 divided by 7.75. And your solution is that T is compute to 2.58. One other thing I want to point out that this doesn't always happen on a calculator. If you're writing out the formula by hand and plugging numbers in, make sure you write things neatly. Because if you forget that something's in parentheses or if you forget that something is part of the numerator, you could mess up the entire operation. So be very, very careful 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.