Welcome to the presentation on averages. Most likely averages is a concept that I’ve actually used Before, perhaps not in a mathematical fashion. But people will talk about, average voters want Politician to do this, or average student in a semester He wants to get out early. So maybe you are already familiar Average concept. And you probably already intuitively knew that Average is just a number representing different values It may be a group. But this can be represented as a single number compared to a given All values \u200b\u200bare different. And let’s give a few examples of how to calculate On average, you might already know how to do this. So let’s say the numbers were one, three, twenty five. And I asked you, what is the average of these four numbers? Well, what we do, we are literally fair Add numbers setting. And then divide by the number of our numbers. So we say one plus three four. So let me write this. One plus three equals three plus five plus twenty, let’s see one plus three four. Four plus five is nine. Nine plus twenty out of twenty nine. And we had four numbers; one two three four. So four goes to twenty nine. And it goes, twenty seven, twenty eight. And then we have ten, I didn’t have to do that decimal point There, oh well. Two, eight, twenty five. 34 00:01:36, 91 -> 00:01:40, 88 4 goes even at 7.25 times 29. So the average of these four numbers equals 7.25. And we kind of view this, 7.25, as one way to represent These four numbers without having to list these Four numbers. There are other protests that you will learn later. Like the situation. You also have the medium that we will talk about later, It is actually the same as the average. But the average is only one number that you can use to It represents a group of numbers. So let’s do some problems that I think will be Be close to your heart. Let’s say on the first four tests of an exam, you got a newspaper Let’s see, you got eighty, eighty one. Eighty-seven, and eighty-eight. What is my average in class yet? Well, all done add an assembly of these four numbers. So I say, eighty plus one eighty plus eighty seven plus 88. Well, zero one plus one. One plus seven is eight. Eight plus eight from sixteen years old. I just ran eight miles away, so I’m a little tired. And four and eight, this is thirty two. In addition to thirty one three. Now we can divide this number by four. Four goes to three hundred and thirty six. Thirty three minus thirty two is one, sixteen. Where the average equals eighty-four. So it depends on what school you go to either from A, B or C. So, my average is after the first four exams so far eighty four. Now let’s make this a little bit more difficult. We know that the average after the four exams is four Examinations, which are equal to eighty-four. If i were to ask you what do i have to get the next test to Average eighty-eight, average 88 in the category. So let’s say that x is what gets the next test. So far what we can say, is that the first four exams, and me You could either list out the first four exams you took. Or I already know what average. If you do not know the sum of the first four exams Going to eighty four four times. Now I would like to add, what gets the exam Vivith, x. I am going to divide that by all five exams. So in other words, this number is average Of my first five exams. We just calculated the average of the first four exams. But now, we can summarize the first four exams here. We add what you got for the fifth exam, and then we divide Five, because now you average five exams. And I said that I need to get in at 88 in the class. Now we can solve for x. Let me just make some space here. So, eighty-eight five times, let’s see. Five times eighty four hundred, even one hundred and forty. You see that a hundred and forty equals four times eighty-four, we just are, and it is Three hundred twenty plus sixteen of three hundred and thirty six. Three hundred and thirty-six plus x equals one hundred and forty. Well, it turns out if you subtract three hundred thirty six from both sides, You can get x equal to one hundred and four. So what if you don’t have a test that has some reward problems on it, Impossible maybe you can get an average eighty eight ah Class after the next exam only. You will have to get a hundred and four and on this next exam. And let’s just look at what we just did. We said, after the four exams we had eighty-four. What should I get for this next exam Average Eighty Eight In the class after the five exams? This is what we had when we got x. Now, let us ask another question. After the four exams, I said, after the four exams, I said The average was eighty-four. If you say there are six exams in class, The highest score I can get is a hundred exam, what is A higher average can be completed in the category if it is already Serious study and get a hundred on the next two exams? Well, again, what will we want to do assuming we get One hundred for the next two exams and take then the average. So we have to solve all six exams. So we will be average six, even at The exams average time eighty four. And this only dot times. Popularity will be a plus, and there are two more exams, right? Because there are six exams in the class. I am going to get a hundred in every country. Even that two hundred. What is this average? Well, four times eighty four, we have already said, it is three hundred and thirty six. Plus two hundred over six. So that’s five hundred and thirty six over six. Six goes to 5:36 am. I don’t know if it gives myself enough space. But six goes to fifty three, eight times. forty eight. fifty six. Nine times. Nine times six to fifty four. Minus six twenty-six goes to the newspaper so we’ll actually see it 89.333333, it goes on forever. Repeat up to 89.3. So no matter how hard I try in this category, the best I can do. Because I only have two exams left, even if I were to get One hundred for the following two exams. Class 89.333 can be completed on average. Hopefully, I think some of this might be a little bit A bit for you to review. The verb was a kind of feeling which is on average. Hopefully, these two problems will continue not only you are studying How to do some algebra problems that are average, but they will Also the instructions you can find out how well you should do on your own Examinations to get A in your class in mathematics. I think you are now ready for the average module. Enjoy.