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2014 Top Albums (Based on U.S. sales) Of all of the U.S. album sales 1989 (Taylor Swift) accounted for $25 \%$ of sales, Frozen (Various Artists) accounted for $24.1 \%$ of sales, In the Lonely Hour (Sam Smith) accounted for $8.2 \%$ of sales. What is the probability that a randomly selected album was something other than these three albums?

Uh huh. And question 138. You're given a really large data set of representing the number of albums sold in the US by top producing artists as of 2000 and eight would be really interesting to see how that's changed in the era of digital streaming. But the first challenge and these questions is to access the data. So the way that I was able to access them was going through the digital edition of the book to the supplements page to the bottom left. You'll see the link there for the wise website. Make sure you get the right edition and you may want to download The Excel files for this question, because this data set comes in two columns, one with the name of the bands and one with the number of albums sold. And that's not easy to import into your other statistical calculators. So I open that file in Excel, copied only the numeric portion of the data, put it in a new sheet and saved it as a comma separated value a C S V. File, which allows me to use it in other places. So that's the file. I'll be using here. The single column numeric data saved again N S C S V file. And we'll be using classical because it's very flexible, easy to use and easy for you to access. You should be free to access that. So we do one little work around. We do have to begin by importing it as a table. And you can see I've already said at the side here, so make sure you can find your data. This comma separated value file can't open it. You see, it's got 239 roads, faces a very large data set, and you can see a very wide range of going from 10 in our in our lower values up to 170 there. So but we don't want to table to run a list. The first thing we need to do here is to redefine our values as a list, uh, 239 items on our list. The next thing we do is to tell that we want to box. I noticed that it was what we're going for. You can also find this under the menus down in the bottom. Right hand, Understand And if you'll notice, Right, So we have this really spread out thing. So chances are we've got some outliers here we need to deal with. Okay? So let's see if, actually, if it will do that for us, exclude the outliers. So let's see what happens. That nice look at that. It readjusted them for us. Okay, If you want to calculate them yourself, you use your portal value, so you do. Q one minus 1.5 times I Q R, which is Q three minus Q one. Okay, just to double check, Demonstrate. Um, so you do 13.5 minus 1.5 times, and we could just type in that difference and start doing it. You have this time, right? But you can see that getting actually negative value there. So there's no way I got outliers have got in. Let's go ahead and check it for the upper end. So we would change it to 27. 28.75 Bless the difference. Interesting in either gonna need fraction here. Um, curious. What that is is a decimal. I'm not sure why. It's giving me fractions. 400 divided by eight though, is about five. Because I know a 10 spot. It was about 50. Because I know eight times five is Yes, I see 40. So, 50 and you can see that a little more than 50. Here is my max range. Everything about 50 is 51 or 52. There is considered an outlier, and you can see it's got a 20 item list here so you can actually pop that one out. So see that ol under right about courthouse? Click that and you've got that whole list of 20 that you need to write down as the outliers for this particular graph. Okay. And then, um, you've got to interpret all your different data so you can say things like, um, you know, the top producers of albums are taught to sail. Album sales generally max out at $51 million or 51 million albums sold. Check the wording of the problem there. But according to the statistical analysis, there were 20 bands who sold even more than that, you know, and were considered statistical outliers among the top producers. Okay. So interesting to go back and see which bans those were. You can also say, um, things like the top 25% statistically sold more than this. $28.75 million million albums. So, um, so give us a minute interpretation there, as your teacher is looking for, you could write paragraphs interpreting each version. Remember the I. Q R Report Ranges Q. Three mice you once you can say the middle 50% statistically so, but this one does require interesting comments that you do end up with 20 outliers if you're being. If you're following the rules as provided, that's all for question. 1 38.

Oh, question 1 38 gives us a really large dataset showing the number of albums sold by the top produced by some of the top producers sold in the U. S. And, um, the interesting thing about this data set is that you get a two column set of data where you have the name of the band or artist in one column and then the number of sales in the second column, and you only want the data. You can only work with the data in that second column, or they might want to look at the band names for curiosity. It'll be really interesting to see how this data has been updated, Um, since this book was put out. So we're following this procedure in layer letter B down here about how to convert this. So look for your book. Find the supplements page, find the wise Web page link at the bottom left. Make sure you choose the correct addition for your book, and you'll actually want to download the Excel file versions for this question and, um, then copy and paste, copy the numeric column into a new workbook and based engineer or work and save it as a comma separated value file. So we'll use that as we go over here to classical. We'll go to this nice little plus sign clip table import, and choose the information for question 1 30 eight. And as we have those 200 plus data points there that we could see if we wanted to. But that is the data set we're interested in. We're first going to redefine it as a list instead of a table. So l one equals x one there. And then we're going to ask it to create a plot of that data. And we want to see the court trials. So click that portal thingy and we want to leave out the outliers. So we're gonna ask it to exclude are outliers. So adjust your screen as navy so you can see it all. So remember, you can go to the slider things in the top, right, And you can set the window manually there if you don't have a touch screen. Um, I'm just squeezing this one. Wow. Look how long it is. So that's really interesting, right? Um and this is with the outliers excluded. It would have been even longer if we had not. Okay, so we're really having to pinch in here trying to make it tall. We may have to do this one manually, there to get the idea. Okay, there we go. There. We're all seeing it together. All right. Look at all those outliers. You have 20 statistical outliers on this data set, which is really interesting. Um, so how they choose that tells you that it's rare, right to have, um, those extreme sales. Most artists have much less extreme sales. Okay, so I'm gonna comment on that in your interpretation. So, um, just remember, you calculate those outliers right by doing q three minus Q one and multiply it times 1.5 1.5 times at 28.75 behind a 13.5. That's kind of your adjustment number. That 22.85 And you add add Add that to the third quartile to that 51 to put you up at, like, 73. Right? Is the statistical max there and subtract it from the 13 point I was actually usually negative numbers. So no lower bound, um, out large, but lots of upper bound outliers there. So when you write up your interpretations here, um, you definitely want to emphasize that you want to say it. Statistically, the maximum value that that artists can expect to sell with their records is like 51 million. Remember, these numbers represent millions, I think double check the wording of your question. Um, so you can say, But there have been 20 you know, outlier bands or artists, and you can go back to the original Excel file and look those up. And so you see which bands those are for your own curiosity sake, but definitely going to list them. Um, and you could say the median you comment on the median is always interesting. Is 18.75 or you can say the middle statistically the middle 50%. You know, it's between 13.5 and 28.75 million albums. Soul. Okay, so you have come with a series of comments interpreting the data that you have been given. That's all for question. 1. 38

The system of equations Using the substitution method. We were given a bar graph, but I've changed into a chart so you can see the numbers a little easier. We have also been given these two equations y equals negative. Five. Sorry, negative 95 X Plus 7 70 y equals 219 x plus 142. And that is our system of equations. So for part A, we just solve the system of equations. Since most of these are equal to y, that means they're equal to each other. So have negative negative 95 x plus 7 70 equals 219 x plus 1 42. I'm going to move all the constants to the left side and the X terms of the right side. So 778 minus 1 42 is 628 and to 19 plus 95 is 314 x. So if we divide by 349 best sites, we'll get X equals two. And this unit is years after 2000 and four. So we'll take this X value and plug it into either the equations I'm gonna choose. The second one will have y equals 219 times two, also 142. So why equals 438? Also 1 42? And why equals 580? So this is how many album sales and digital sales they had in 2000 and six. So part be asked, when did the track sales catch up? The yellow sales? That is two years after 2004. So 2000 and six, and it asked how many digital checks are sold? Its 580 uh, and that is the millions. 580 million. And how many albums are sold again? 580 million, since it is the equilibrium. That is why both the digital tracks and the albums sold are the same value.

Alright for this question, we have been given a table. Now. If a new book or edition is selected at random, we have to find the probability that it subject area is one of those specified. It's either art or music. In part we want to find either art or music. So from the table I can see that art or music means in addition. So 4481 plus 1614 4481 plus 1614 divided by the total the total of all the subjects. It is 119923 119923. And this turns out to be Around 0.051 0.051. This is the probability for part a. How about for part B For part B. It is neither science nor religion, which means it is either art, business, history or music. So I add all of these. So this is going to be or I can also write this as one minus the probability that it is from either science or religion. So it is 7032 plus 66597032 plus 6659 divided by the total. What is the total? Total is 119923 And this value turns out to be 0.886, or 88.6%. This is the probability for party. This is our answer.