![]() ![]() They'll give you the numbers in a jumbled order, and then you yourself have to put them in order, and then find the median. And often, incidentally, the test will not do that. No, we have to put the list in order from smallest to biggest. Okay, the median is the one that happened to be sitting in the middle of that jumble. So, we can't just write them in any jumbled order and then say. Technically, the median is the middle number on an ordered list. We have to put the list in ascending order first, that is from smallest to biggest. The median is the middle number on a list. ![]() So that's how we answer that question, purely thinking about sums. Then we should get, we get 83, and of course that has to be Burt's grade. Well, if we subtract Alicia's score of 77. So Alicia's score and Burt's score must add up to 160. So the difference between them should be the sum of the score of Alicia and the score of Burt. What's the difference between them? The only difference is we added Alicia's score and Burt's score to the other 18 scores. Well think about that, the old sum and the new sum. Well now the new sum of all 20 students, that's going to be 20 times 71 multiply that out that's 1420. I'm just going to take 18 times the mean of 70 multiply that out and that's 1260. So first of all, the old sum, those 18 people. The key to this question is simply thinking about the sums. If Alicia got a 77, then what was Burt's grade? All right, so a lot of people would find this a very hard question. Alicia and Burt then took the test and the average of all 20 students was 71. Okay in a class, 18 students took a test and had an average of seven, 70. Pause the video and then we'll talk about this. So this second form, it's really underappreciated how powerful this form is. Thinking about sums is often the key to many questions about average or mean. In other words, the number of people on the list times the mean has to equal the sum of the entries. ![]() If we just multiply both sides by N, we get N times the mean. Notice that this formula is also quite useful in the following form. We can write the formula as mean, equals the sum of N entries divided by N. In general, on a list with N entries, we add up all the entries, and then divide by N that's the mean. To find the mean, say, of seven numbers on a list, you would add up the seven numbers, and then divide this sum by seven. A mean is, is, is simply an ordinary average. The two most important measures of center are mean and the median. Well, such numbers are called measures of center, and that's what we're going to start talking about in this video. ![]() For example, if we had a list of the household income of everyone in the United States, we'd wanna know, what's one single number that would be representative, most representative of that entire list. So one of the most fundamental questions we can ask about a data set is, what single number is most representative of the set as a whole? And this turns out to be very important in real world statistics. So we'll get some data and just be asked about that, this data. For the purposes of the test, statistics consist of tools, for making sense of data. In the big picture, statistics is a rather broad subject, but we only have to know a few things for the test. Where \(f\) is the frequency of the interval and \(m \) is the midpoint of the interval.Now we can start talking about statistics. ![]()
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