But man, guys, one of the best things about box plots is it's a fantastic way of comparing two sets of data. Why? Because box plots can literally be drawn side by side. See, the issue with histograms is you can only draw one histogram at a time, versus box plots can be drawn on top of each other, drawn next to each other, which allows for excellent moments of comparing. So that's what we're going to do now. What we're doing is we're looking at maximum temperatures that occur in Provo and in San Francisco, and what I have are three statements. And I want us to determine for each one of them: are they true or false? And there's going to be one keyword in each one of these statements that's going to help us identify what we'll use from the box plot to determine if these statements are true or false. So let's do the first one: Both cities have similar typical temperatures. The key word here is 'typical.' And I want us to go back and remember the earlier part of Chapter 3, 3.1, and 3.3. And let's go back and remember 'typical' represented something. It represented either shape, center, or spread. Which of these three words did 'typical' represent? It represented center. Let's go back and remember the word 'typical' was the interpretation word we used for both mean and median. But, so then that's the next question: When looking at my box plot, which center am I given? Am I given the mean or am I given the median? Yeah, the box plots give us median. So what we want to do is we want to compare the medians. We want to compare the medians. So let's zoom in a little bit. Let's look at San Francisco, the top graph, and we can see here that the median is maybe 62 degrees. It's about 62 degrees Fahrenheit. And if you look at the median for Provo, that one looks probably closer to 65. And so now that we were able to zoom in on the graph, zoom in on the graph, know that we want to compare 'typical' by comparing medians. Let's go back to the question: Do both cities have similar typical values? Do both cities have similar medians? True or false? Yeah, 62 and 65 are very, very close to each other. Very close. All right, great, let's try another one. Let's try another one. Example B: Both cities have fair symmetric distributions. When you guys see the word 'symmetric,' what is that going to trigger in us? Shape, center, or spread? What is that going to trigger in us? Shape, center, or spread. Yeah, definitely triggers in our brain 'shape.' But let's go back and remember that when it comes to box plots, you are using the longer whiskers, you are using those outliers to help you identify, in essence, where the tails are when looking at skewed graphs. All right, let's remember that when it comes to looking at box plots, you are looking for the longer whiskers and outliers to identify the tails of skewed graphs. So let's look at the San Francisco graph. Notice on the San Francisco graph, on the right, we have a longer tail combined with outliers. Notice how in the San Francisco graph, the left-hand whisker is pretty short comparatively to the right whisker plus all of the outliers. So in this case, given that the San Francisco graph has, on the right, both a longer whisker as well as outliers, what do you guys think that's going to mean in terms of shape? Do you think it's going to mean this graph is symmetric or do you think this is telling us my graph is skewed? Which one do you think? The fact that on the right we have both longer whiskers and outliers, is this telling us my graph is symmetric or skewed? Yeah, it's ultimately going to mean that my graph is skewed. And not just any skewed, but the fact that all of the longer whiskers and outliers are on the right is telling me my graph is skewed right. All the right goes together. So let's go back to my true/false statement. Let's go back. Both cities are symmetric. Is that true or false? Are both cities having a symmetric graph here? Definitely not. No, this statement is false. All right, we've talked about center, we've talked about shape. You guys probably guess what's happening with the third statement. 'Provo has a much greater variation in temperature than San Francisco.' Variation, guys, remember, always represented the idea of spread. And by this point, we've learned standard deviation and IQR. Now, again, we're looking at box plots. And when you're looking at a box plot, what are we given? Are we given standard deviation or are we given IQR? When you look at a box plot, the whiskers, the box, are we given standard deviation or are we given IQR? Yeah, we are given IQR. And can you guys remind me again, can you remind me what about the box plot represents IQR? Yeah, the distance from Q1 to Q3, which is the length of the box. Let's go back and remember, the length of the box represents IQR. So on top, we can see San Francisco's IQR, that small length of the box. On the bottom, we can see Provo's IQR, that length of the box. And so let's go back then to our question. Question is asking: Does Provo have a much greater variation? So what we're asking here is then: Does Provo have a greater IQR than San Francisco? Looking at my two graphs, comparing San Francisco's little box versus Provo's big box, does Provo have the greater IQR? True or false? True.