Understanding GraphsDate: 10/30/2002 at 09:15:23 From: Jenna Subject: Graphs in real life Dr. Math, I was wondering how a lot of our math problems and formulas are brought into real life situations. I don't think algebra occurs too much in real life. I don't think it works too well, like using graphs in real life situations, because they usually only come up when you have to try to help somebody with their homework. Thanks a lot. Sincerely Yours, Jenna Date: 10/30/2002 at 11:51:47 From: Doctor Ian Subject: Re: Graphs in real life Hi Jenna, The answer to your question depends on what your 'real life' is like! If you sell shoes during the day, and then go out drinking and dancing with your friends at night, then you aren't going to have much use for algebra. On the other hand, if you write computer programs, or design bridges, or navigate spacecraft, or try to develop scientific theories, then you can't go more than about 15 minutes without using algebra in some way. But the answer to your question also depends on what you mean by 'occurs'. Let me give you an example. Suppose you pick up a copy of _USA Today_, and you see a graph that looks like this: | * | | | | | * | | Terrorist | Incidents | | * | +---------------------------- Year 2000 2001 2002 Now, what conclusions should you draw from this graph? That terrorist incidents went up by a lot and then down again? Sure, but in order to really make sense of this graph, you have to know what the actual values are! So let's add those to the graph: 120 | * | | | | * | | | Terrorist | Incidents | | 110 | * | +---------------------------- Year 2000 2001 2002 Now the values are there, so we can see that the increase wasn't all that big, but the picture still looks pretty dramatic, doesn't it? Well, what if we start the axes from 0 instead of from the minimum value? That puts things into context: 150 | | | | * * | * 100 | | | | | Terrorist 50 | Incidents | | | | 0 +---------------------------- Year 2000 2001 2002 Things look a little less dramatic in this version, don't they? Now, suppose you're a member of Congress, and you're trying to get funding for a new federal anti-terrorism office in your home district, which will mean more jobs and money for your constituents, which will mean more votes for you when you run for re-election. Which graph would you rather show people? The first one, right? And do you hope that the people you show it to will know enough to understand what you've done? Probably not. So, how _do_ you learn enough to understand what makes the first graph misleading? Well, the way you learn how to _read_ graphs carefully is by learning to _make_ graphs. That's how you learn what it means to plot a point relative to some axes. It's how you learn how different kinds of curves are shaped. It's how you learn where and how often to place tick marks, and a hundred other little details. In order to _do_ these things, you have to make decisions. And in order to make decisions, you have to be aware of the possibilities. And it's being aware of the possibilities that allows you to really understand not just the graphs that _you_ make, but graphs made by other people as well. In short, you can't really understand how to _read_ a graph unless you know how to _make_ a graph. Similarly, you can't really understand averages unless you know how to compute them. And you can't understand any argument that makes use of numbers - which these days, includes just about all of them - unless you know how to generate those numbers. Otherwise, you just have to trust people not to try to take advantage of your ignorance, in much the same way that very young children have to trust the adults around them not to lie to them. So, if you pick up a newspaper and start reading about how 42% of the people polled think such-and-such, or when you see a graph that is supposed to illustrate some trend, does that count as an 'occurrence' of algebra? In my book, it does. You may feel differently. It depends, I suppose, on how trusting you are, and how much you object to having other people fool you. I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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