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. Now we can start talking about statistics.

Median mode and