 Statistics and Excel. Issue with five number summary and box plot. Got data? Let's get stuck into it with statistics and Excel. Although we'll be using one note here, but we're going to talk about Excel too. You're not required to, but if you have access to one note, we're in the icon left-hand side one note presentation 1422 issues with five number summary and box plot tab. We're also adding our transcripts so that you can go to the view tab, immersive reader tool, changing the language if you so choose being able to either read or listen to the transcripts in multiple languages using the timestamps to tie in to first a word from our sponsor. Actually, we're sponsoring ourselves on this one because apparently the merchandisers, they don't want to be seen with us, but that's okay whatever because our merchandise is better than their stupid stuff anyways. Like our CPA six-pack shirts, a must-have for any pool or beach time, mixing money with muscle, always sure to attract attention. 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We're going to do some of our standard stats on both data sets including the mean or average, the min, quartile one, median or quartile two, quartile three, and the max. We'll also create a box and whiskers for both data sets, otherwise known as a box plot, and we will see that although both data sets are very different, we're going to come up with similar stats or the same stats and basically the same image in the form of a box plot. Now this is given to highlight the fact that sometimes these stats, although important and very useful, may not be all we need in order to get a real grasp of the data, especially when we're thinking about the spread of the data. How is it basically populated say around the middle point? So if we look at these two data sets, they've been specially put together so that all these stats are going to work out like this, but the general concept is the idea here. So we've got data set A, we've put them in order from smallest to largest, 50, 75, 75, 100, 100, 125, 125, 150, data set B, 50, 75, 75, 75, 75, 125, 125, 125, 125, and 150. Now if I look at our stats then for data set A, we can take our average, which is simply adding up all the numbers, and then dividing by the count, or we can use the Excel formula, the average formula, we get to 100. And then if I do the min, meaning take the smallest number, we can see in data set A it is 50. And if I do the calculation in Excel, it would be equal to min, and that would automatically give us the 50, quartile one. So now we're picking the middle number in the first quartile, breaking it out into quartile 75. And if I was to do that in Excel, I would have the quartile function, it has a second argument, making sure that we put the comma and then the one, picking up the 75. Then the median, or quartile two, is the middle number. So we order it all and pick the one in the middle, which is going to be the 100. We can also do that with the median formula or function in Excel, or we can use the quartile function, and then comma two. Median function is usually the one that's going to be used. It's easier. It's faster. You only have one argument instead of two to do it. And then quartile three is going to be like the middle point of the last quartile 125. Same quartile formula, but the argument on the second argument is a two if you did that in Excel. And then the maximum is 150. 150. Now, and that would be a max formula here. Now, if we did the same thing for B or this, I'm sorry, this is going to be the box and whiskers. So we've got our box and whiskers representing our numbers here. And you can see these numbers being represented, the 100 average is the same in this case as the median, the 50, the 75, the 125 and the 150 125, and the 150. Okay, so now I think I put it underneath here. Let's go to data set B. So here's our two data sets again. I'm focused on let's just open data set B this time. So now if I look at data set B, the average if I took the average and added up data set B, I once again get to 100, which is the same as what we had for data set a I'll just open both of these. So they come up the same. It's like, Okay, well, that's kind of weird because the data sets are clearly different. Right, these are different data sets pretty dramatically different. So if I go to the men, I get to the same number. So it's like, Whoa, is this like this? Am I is this just the same numbers the same data set? Let's take a look at quartile one. If I took quartile one for data set B versus data set a I get the same number, which is like that's weird. And then the median, if I look at the median, I get the same number, the middle point. And then if I look at the quartile three, again, I get the same number down here. And then if I look at the maximum, I get the same number. And if I was to then do the do a box plot, because I got all the same numbers, you would think the box plot would basically look the same. So here's the box plot for data set B that we saw versus data set a. Now, if I look at the histograms, they they do show us the difference, right? So the box plot isn't giving us because this is that kind of five numbers, but the histogram does give us that because it gives us that kind of middle point. So the histogram gives us an idea if I break it out in a histogram, I'm saying, well, these are substantially different. When I think about these data sets in terms of how the data is spread around that middle point, so you can see here, you've got that middle point, you know, looking looking more like a, you know, the curve in the middle, it's popular, more the data sets in the middle, and then they spread out this way on the right hand side. And the middle point, or the average and and the median, both coming out to be a 100 in here somewhere down here, although you get the same median and average, there is nothing in this middle point and the data is still over to the side, but we still get all the same numbers, we still get the same average, we still get the same, you know, middle number even and the quartiles. Now, this isn't likely that you're going to get all the same numbers, right? This is a pretty specially designed data set. So all of these numbers line up, but you can get the idea here. The idea is that these numbers, although quite important, useful to be calculating, don't always give you everything you need, especially with regards possibly to the spread of the data, like around the center point, which is going to be our point of focus when we get to things like the standard deviation and the variance. So these two box plots, you can see are exactly the same for data B and data A. And then the histograms do give us that indication. And so our focus is in on this kind of concept right now with the spread, which we want to be able to summarize. It would be nice numerically if we could as well as pictorially with like a histogram. And so we'll get into some calculations based, which will be the, you know, the standard deviation and the variance in future presentations.