Hints for Lesson 4 Catalog Problem Set

PRESENTER: When I try to picture really big or really small numbers, I like to break it down into something else that I can understand a little better just so that I have some idea of what's going on. 

In this lesson, we read a paper by this group of scientists, and they estimated that between the 1950s in the 1990s, Alaskan glaciers lost an average volume of around 50 cubic kilometers of water every year. And then between the 1990s and the early 2000s, those same glaciers lost closer to 100 cubic kilometers per year of water. Do you have any idea how much water is in a cubic kilometer, much less several cubic kilometers? Let's do a little calculation to try to put that into perspective. 

What if I took one cubic kilometer of water and I wanted to apportion that water out for the entire world so that every single person in the world would get some of that cubic kilometer. How much water would everybody get? Well, we can do that calculation. 

If I have one cubic kilometer, that is a box with 1,000 meters on a side. So that equals 1,000 times 1,000 times 1,000 meters. That is 1 billion cubic meters. And I also know that in one cubic meter, there are 1,000 meters. 

So if we have 1 billion cubic meters, and there's 1,000 liters in each cubic meter, that means we have 10 to the 12th meters of water in a cubic kilometer. Now's a good time for me to give a shout out to my 12th grade government teacher from Blacksburg High School, Karen Colson, who explained to our class that she thought that one of the reasons Jimmy Carter did not get elected to a second term is because he tried to convert this country to the metric system. And we all know how well that worked-- not very well. So I don't think most people can actually even picture what a liter probably is. But all of us non-scientist, milk-drinking Americans probably know what a gallon looks like. It looks like this. And there's about four liters in every gallon. 

So if I have 10 to 12 liters and I divide that by 4 to get gallons, then that's about 0.25 times 10 to the 12th gallons. And as of late 2012, there were about 7 billion people in the world, so we just have to divide this number by 7 billion. And we'll figure out how many gallons of water everybody is going to get. 

And that number is this. We can write this in a much more normal way by just moving this decimal three places over to take care of this exponent. And what we find out is in each person in the world gets about 36 gallons if we had one cubic kilometer of water and we apportion that up over everybody. 

But remember, in this paper we're not talking about one cubic kilometer of water. We're talking about between 50 and 100 cubic kilometers of water every year. That is a lot of water, my friends.

PRESENTER: In this video, I'm going to give you some tips for how to organize your data to make the plotting in this problem set easier. So your data file probably looks like this. This is just a text file. And for each earthquake, in the row, there's a bunch of information about it. There's the day that it happened. There's the time, the latitude, the longitude, the depth, the magnitude, and then some text information. 

So what you want to do is just grab out the magnitudes, because we don't really care about anything else at all in this. Just to make our plot, all we want is the magnitudes. So I use [INAUDIBLE], but you can use something else, or nothing, if you'd rather just work with this entire big data file. So I make a new file that just has the magnitudes in it, and here it is. So here's all the magnitudes in order. 

And now I'm just going to use Control-A to copy the whole file-- or select the whole file and then Control-C to copy it. And I'm going to open up a spreadsheet document. I use Numbers, because I'm a Mac user, but it's very similar to Excel. So if you're used to that, this is going to look normal to you. And then I'm just going to paste in the contents of that file right into this spreadsheet with Control-V. And there are all my earthquakes. 

So they're all sitting here in this column now. And the thing I'm going to do to make my life easier is I'm going to choose to sort them in descending order, having the largest magnitude earthquake moves into spot number one-- it's a 4.3-- and the smallest one moves into the spot in the bottom. I'll move this file up so you can see it better. But there's 180-some earthquakes in my catalog, and the smallest one is a magnitude 1. So there we are. 

Now, there's only 180-some earthquakes in this catalog, so it's conceivable that you could count them all by hand, because you want to populate an x and y table with the magnitude and then the number of earthquakes greater than or equal to that magnitude. So it won't take you too long to count them by hand. But if you had a really, really big data file, like 20,000 earthquakes, you would not want to count them by hand, of course. 

So look at how these are sorted, and see if you can think of a way to count them without doing it by hand. And if you're still stumped, then watch the next video.

PRESENTER: In this video, I'm going to explain to you how to construct your xy data pairs so that you can make the plot that shows the frequency magnitude distribution of these earthquakes. So let's go back to the spreadsheet here. I've got my table of values that shows all the magnitudes of the earthquakes that happened in 1975 in the New Madrid region. And I have them sorted in descending order. So the largest magnitude earthquake is up here in spot number one, and the lowest one is down here in spot number 183. And that's the total number of earthquakes that there were in 1975 that were recorded. 

Now, I've made a second table of values over here. And there's is one column called Magnitude and one column that that's says number of earthquakes greater than or equal to that magnitude. And these are going to end up being the x and y values of the plot that I'm going to make. And we're going to get these x and y values by doing some manipulation of the original data over here. 

So my x values, I've already just stuck them in. They should go from the largest magnitude by increments of 0.1-- so you can see that, right?-- down to the lowest magnitude that you have in your catalog. And my lowest magnitude is 1.0. So there that is. And now we want to find at each magnitude how many earthquakes are there in the catalog that have that magnitude or a higher magnitude? 

That's why we sorted these earthquakes, so it'd be easier to figure that out. OK, so let's go back to the catalog and start with that. So the largest is 4.3. And how many are there of those? There's just the one. So 1, easy. OK now, this is the part where you have to think just a little bit. 

The next earthquake down from 4.3 is 3.3. And there's three of those, right? So what we want to do is write down the number of earthquakes that are at least magnitude 3.3 in this catalog. And there are four of those, right? Because there's this 3.3, this one, this one, and the 4.3. All of those earthquakes are 3.3 or greater. 

Now, what we can see is that the actual number corresponding to the last 3.3 magnitude earthquake is the number we're looking for, right? So we go over here to our xy table, find 3.3, and write in a 4. Now, what we do with these blank spots up here? Well, let's just think about it. How many earthquakes are at least magnitude 3.4 in this catalog? 

Well, there's just one. There's just the 4.3 that's larger or equal to 3.4, right? So there's just one. And now I hope you can see that you could fill in a 1 in each one of these boxes as well. In fact, you have to. That's correct. All right, so let's go back to our catalog now and go to the next earthquake down. 

The next magnitude down is 2.8 and there's two of them. So we can see that there are six earthquakes in this catalog at least as large as magnitude 2.8. So let's go over here now. And we write 6. Then we fill in the blank ones above 2.8 in this row with 4's, using the same logic that we used to fill in the 1's above magnitude 3.3. 

OK, let's go back to our catalog. Here's 2.7. There's just one of those. This is easy. So we read off a 7 right there. Hopefully you can see the pattern now. There's two of these. There's nine earthquakes in the catalog that are at least magnitude 2.5 or greater. 

So that means there's a 9 here, and that means above that where there's a blank spot, we put in a 7. There's at least 10 earthquakes in the catalog whose magnitude-- sorry, there are exactly 10 earthquakes in the catalog whose magnitude is at least 2.4. Put the 10 here. There are exactly 20 earthquakes in this catalog whose magnitude is at least 2.3. And I think you can do the rest of this by hand yourself.

PRESENTER: Now I'm going to use the table values that I just made to make a plot of this data. And Numbers makes it pretty easy to do that. I just have to select this table and figure out what kind of plot I want to make. I like the scatter plot. And now it's plotted the x-values in this column versus the y-values in this column. 

So let's look at our chart here. Now, first of all, we want this to be a log-to-log plot. Magnitude's already a log scale, so that's fine. You can leave that alone. We want to change it so that the y-axis is a log scale, and we can do that right here. 

And then we want to clean up some things about this plot, because "Chart 4," for example, is really not a very good title. Let's call it something else that's more meaningful. We don't need a legend, because we're only plotting one piece of data. So let's get rid of that. 

And then let's use the Chart Inspector over here to figure out how we're going to label our axes, because you have to label your axes, otherwise people don't know what you're plotting. 

What's on the y-axis? The y-axis is showing the number of earthquakes greater than or equal to some magnitude. And then the x-axis is magnitude. We'll just call it M. And now I can clean this up a little bit. Also, I don't really like the data symbol. It's just my personal preference to use something besides a plus mark. Let's connect the points. 

There we go. That's it. You've made your plot. Looking good.

PRESENTER: All right, so if you are using Excel, not Numbers, and you've had difficulty figuring out how to make a plot a log log axes, here's how you do it. So this is a plot of just some random data, this has actually nothing to do with the [INAUDIBLE] data or anything else. And I'm just doing this for a test, because you can see it's got this ugly legend and it says, "series one," which I do not like. 

OK, so I got this plot, I'm in Excel. And if I want to make the y-axis log, what I would do is, I make this plot active and then click on the axis line, so then this thing that says "value-- y-axis" pops up. And you can see these two squares you here so you know that you selected it. Now up to Format and select, Selected Axis. Then this other little window pops up. I'm [? scootching ?] it in so you can see what it says. And you want to click the buttons that says Scale. And then right down here, you can choose Logarithmic Scale. OK. And see how this plot has changed. You can do that for both axes too if you want. So that's how you do it.