Misleading graphs

[Minoosh]

I'm working as a long-term substitute for 3 math classes. Yesterday I gave students a very basic graphing problem. A cheese pizza costs $5; each topping is $1. I was looking for a y intercept of 5.

Some kids started their y axis at 5, though. As long as it's labeled, I see this as misleading but not necessarily wrong. I gave them credit but made them fix it. They were arguing with me about it, which is a good thing, but I told them we were using the graph to communicate and that this was too misleading.

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

 

[psionl0]

Make your instructions clearer.

 

[Minoosh]

Make your instructions clearer.

Many are not actually listening anyway

 

[psionl0]

Many are not actually listening anyway

So give them a graph and tell them to plot the points on it. No need to even talk then.

 

[Crossbow]

I'm working as a long-term substitute for 3 math classes. Yesterday I gave students a very basic graphing problem. A cheese pizza costs $5; each topping is $1. I was looking for a y intercept of 5.

Some kids started their y axis at 5, though. As long as it's labeled, I see this as misleading but not necessarily wrong. I gave them credit but made them fix it. They were arguing with me about it, which is a good thing, but I told them we were using the graph to communicate and that this was too misleading.

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

I have to say, that question is bit ambiguous.

If it it were me, I would ask something like:

If the cost of a basic cheese pizza is $5.00 and each topping costs $1.00 extra,

Then:

graph the cost function where the x-axis is used to represent the number of pizza toppings and the y-axis is used the total cost of the pizza, and

find the y intercept of graph, and

find the equation of the cost function.

Answer:

Due to the lack of graphics, I will not show the graph here.

The y intercept is:

5

The equation of the line is:

y = x + 5

To answer your question about the origin ...

There really is no requirement that the origin starts at (0,0).

Usually the origin starts at (0,0) unless otherwise specified, but in some applications the origin can be quite different.

For example, Surveyors of use an origin of (10000, 10000) when working out a survey. That way all of the data collected will have positive values, which makes it easier to work with.

I hope this helps.

 

[Trebuchet]

I'm working as a long-term substitute for 3 math classes. Yesterday I gave students a very basic graphing problem. A cheese pizza costs $5; each topping is $1. I was looking for a y intercept of 5.

Some kids started their y axis at 5, though. As long as it's labeled, I see this as misleading but not necessarily wrong. I gave them credit but made them fix it. They were arguing with me about it, which is a good thing, but I told them we were using the graph to communicate and that this was too misleading.

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

Most graphs of pretty much anything I see in the media are like that. It's intentional, trying to exaggerate a minor effect to make a point.

 

[crescent]

It is not always misleading to do it that way, it sometimes occurs even in good "hard science" peer review lit. If you are trying to visually depict the nuances of a small but significant difference between two populations, then scaling the graph to highlight the differences works well. It may not be done to make the difference appear larger than they actually are, but just to make them visible in a limited space within a report.

 

[bytewizard]

More importantly, where can I get a pepperoni, olive and cheese pizza for $7.00?

 

[Hellbound]

More importantly, where can I get a pepperoni, olive and cheese pizza for $7.00?

Grocery store, aisle 11-Frozen Foods. 2 for $5 special!

 

[Minoosh]

So give them a graph and tell them to plot the points on it. No need to even talk then.

It's a word problem. That alone freaks some of them out.

 

[Minoosh]

I hope this helps.

It does. Thank you.

Grocery store, aisle 11-Frozen Foods. 2 for $5 special!

Little Caesars comes pretty close. I actually have a canned lesson sponsored by Domino's ... with slightly more challenging arithmetic.

 

[Jim_MDP]

Little Caesars comes pretty close.

I doubt they even have olives in house... but CiCi's does.

(damn.. I miss CiCi's, but they're not this far West, certainly not here on the coast. )

/derail

 

[p0lka]

It is not always misleading to do it that way, it sometimes occurs even in good "hard science" peer review lit. If you are trying to visually depict the nuances of a small but significant difference between two populations, then scaling the graph to highlight the differences works well. It may not be done to make the difference appear larger than they actually are, but just to make them visible in a limited space within a report.

yeah, as long as the x and y axis are label correctly then its clear..

 

[GlennB]

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

If you're measuring the progress of industrial output, or exchange rates or similar stuff, then it's damn hard even to say where 0 is You start at a point that's reasonable for the task in hand, and pretty often it can't possibly be 0.

 

[ceptimus]

If you're a politician or an economist, you choose the start and end times of your graph to make the results look as good (or bad) as possible, and you choose the range of the y scale similarly to make the rises or falls in the graph look as dramatic or insignificant as your policy or theory requires.

We often see graphs on the news about, say, the currency market rates or unemployment figures or whatever that show precipitous dramatic-looking climbs or descents - if the y scale on these graphs were chosen to include y=0 the graphs would be indistinguishable from straight horizontal lines.

 

[Lukraak_Sisser]

As others have said, as long as you label it correctly a graph can start at any coordinates you like.
One of the main problems with students is that they don't label anything at all.

It's often worth a few lessons to focus on that so that they can learn to differentiate between graphs ment to explain and graphs ment to mislead. At least we might see less of them here on the forum in a few years defending things like the electric universe of Mill's nonsense which all work with misleading graphs.

 

[Chanakya]

I'm working as a long-term substitute for 3 math classes. Yesterday I gave students a very basic graphing problem. A cheese pizza costs $5; each topping is $1. I was looking for a y intercept of 5.

Some kids started their y axis at 5, though. As long as it's labeled, I see this as misleading but not necessarily wrong. I gave them credit but made them fix it. They were arguing with me about it, which is a good thing, but I told them we were using the graph to communicate and that this was too misleading.

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

Unless I’m misunderstanding what you’ve said, I think your students have displayed excellent creative thinking!

Don’t we all use graphs like that at times? In order to focus on and highlight some movement, not in order to deliberately mislead, but to lucidly and clearly present the information?

Take this graph. I’ve removed the legends (since this is from work, and the specifics of the data don’t really matter to us here) -- but here you have a situation where, if you insisted on starting from (0,0), you’d end up with a very cumbersome picture. *

I don’t know how old your students are, but if these “kids” have by themselves hit upon the understanding that this is merely a convention, and that the convention can legitimately be fiddled around with if the situation so warrants, then surely that’s a good thing?

Of course, they need to realize that you don’t do this for fun (because while fun is definitely good, unnecessary ambiguity is undesirable and confounding), and also realize that this can sometimes be done to distort the information being presented. As you say, that can be a further teaching point.

* Tried pasting a static grab of a graph here, but could not. At least not via a simple cntrl-v. Nor could I make out any button here that might help. Can anyone here tell me if one do it at all? How? (Just asking out of curiosity. That graph itself that I tried pasting, while illustrative of what I was saying, was no big deal, easy enough to conceive of any such graph.)

 

[GlennB]

* Tried pasting a static grab of a graph here, but could not. At least not via a simple cntrl-v. Nor could I make out any button here that might help. Can anyone here tell me if one do it at all? How? (Just asking out of curiosity. That graph itself that I tried pasting, while illustrative of what I was saying, was no big deal, easy enough to conceive of any such graph.)

I believe you can only embed a saved image, either from an image hosting website or from your own pc via the "upload" facility. ctrl-v of a copied image won't work.

Use the "Go advanced" then "Manage attachments" options to upload from your pc.

 

[Chanakya]

I believe you can only embed a saved image, either from an image hosting website or from your own pc via the "upload" facility. ctrl-v of a copied image won't work.

ok, thanks. yes, I figured out the "upload" thing, but one may not always want to do that.

Use the "Go advanced" then "Manage attachments" options to upload from your pc.

eta : Had missed your edit. Thanks, that tip's good. You can put in simple attachments without necessarily giving away more information than you want to.

 

[GodMark2]

I'm working as a long-term substitute for 3 math classes. Yesterday I gave students a very basic graphing problem. A cheese pizza costs $5; each topping is $1. I was looking for a y intercept of 5.

Some kids started their y axis at 5, though. As long as it's labeled, I see this as misleading but not necessarily wrong. I gave them credit but made them fix it. They were arguing with me about it, which is a good thing, but I told them we were using the graph to communicate and that this was too misleading.

Is there any convention that says Cartesian coordinates have to start with 0? Does a graph have to start at the origin? When I see those corners drawn, I assume we're at (0,0). I know that sometimes graphs are misleading on purpose, and that's an excellent lesson to students. But there are other students in the class who might benefit more from being told, "That's wrong; the correct answer looks like this." Just like we tell 5-year-olds that "c" makes a "k" sound. It's misleading, but you deal with the subtleties later.

I see a missed teachable moment here. Instead of trying to tell them why it's wrong or misleading, show them. Make some of your own graphs of the same data that completely mislead: (x,log), (x, exp), (x, -y), y-axis starts at -200, etc. Then have them describe the graphs they see, and then you can discuss why some are misleading, and in what ways.