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Misleading Graphical Displays

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Hi. This tutorial covers misleading graphics. So let's take a look at a graph. The following graph shows yearly sales data for a small company for the years 2007 to 2011. So if we take a look, it looks like it's set up pretty well. So this is just kind of a basic line chart, so it's displaying years on the x-axis and sales in thousands of dollars on the y-axis.

So in 2007, it looks like this small business had $342,000 in sales. 2011, $415,000 in sales. So as you may have guessed, this graph is a bit misleading. So think about why it may be so.

All right, so let's first of all define what a misleading graphic is. So it's a graph that gives a false impression of data. OK, so the following graph is misleading. It looks like the business had a huge increase from 2010 to 2011. So let's just take a look at that again.

OK, so notice it seems like it had a pretty steady increase, and then from 2010 to 2011, it jumped from 380 to 415. OK, so it did seem like 2011 was a pretty good year, and the graph showed a pretty dramatic increase. But now since the y-axis did not start at 0, the vertical distance between $380,000 and $415,000 appears to be exaggerated.

The next graph shows the same data with a more appropriate scale. So I'll show you that now. OK, so if we take a look, it's graphing the same data, but you can see that now if we start our y-axis down here at $0, now, we just kind of see this gradual increase. Yeah, there was a little bit of a spike here, but it's certainly not as exaggerated as it was in the previous graph.

So in this case, there was an issue with the scaling of the graph, and just to make sure what a scale is a scheme to label an axis. So in the first graph, it did not start at 0. In the second graph, it did.

OK, let's take a look now at a second graph. Again, you should be thinking about how this might be misleading. So now, consider the graph for household incomes for a particular neighborhood.

So the income categories here are in thousands of dollars, and then we also have frequencies labeled on the y-axis. So it seems like there's about 50 people in the $0 to $45,000 income level, a little more than 30 people in the $45,000 to $55,000, maybe about 11 or 12 people in the $55,000 to $65,000, and et cetera. And this last category was $75,000 and up.

So again, this is misleading. Since unequal intervals are used for the income category, several categories are misrepresented. So if we think about-- the three middle categories are probably displayed pretty well. They all have interval widths of $10,000. I think it's pretty easy to compare these three income levels.

But now, the first one and the last one, this one is covering a whole wide range of people from $0 all the way to $45,000. Within this bar, there could be people that are making $44,000, but there also could be people that are literally making no money in a year. So there's a wide range of people here, so I would say that's not the best way of representing this group of people.

And then also, the $75,000 up. There could be some people that make a half a million dollars a year, even a million dollars a year, they're going to be way off this chart, but they're just lumped into this one bracket. So this is what we-- this is also not a great way to represent this data, and this graph then would be a little bit misleading.

I've also seen that same type of-- so let's look at that same data represented in another way. This way, you'll see sometimes too. Again, you should be thinking about why this is misleading. So now, down here, I have income categories in thousands of dollars, and I've seen it sometimes where people will just go, well, to make sure that I get it accounted for, from 0 to 45, that's going to be this whole-- it's going to go up to 50, because there's 50 people in that category.

And then 45 to 50, that was about a little more than 30, so that'll be that bar. 55 to 65 was a little bit above 10, so that's kind of like so. 65 to 70, that was almost up to 30, so maybe like so. And then 75 plus went up to a little more than 30. And sometimes, I'll just leave it open like that.

This is also a very misleading way of representing the data. So even though there's 50 people here, 33 people here, the difference here is 17 people in this box versus this box. We can see that this area is way, way bigger. So even though just the height is representing the number of people, this bar looks way bigger than this.

So again, this graph is also misleading. The area in the first bar seriously exaggerates the $0 to $45,000 category. So a perceptual distortion is created by the exceptionally long interval, where a perceptual distortion is a lack of correspondence between what a graph shows about data and how the same data is usually perceived. So in this last example, again, we have a perceptual distortion, just because this bar is so much bigger in area than that bar.

So that's just a couple ways where graphs can be used to mislead the viewer. So make sure that when you're looking at a graph, make sure it is displaying what it should be displaying, and it's not doing so in a misleading way. So that has been the tutorial on misleading graphics. Thanks for watching.

Hi. This tutorial covers a type of graph called a pictograph. A pictograph is a type of graph that has artwork embedded in them. Sometimes the artwork takes place of appropriate labels or numerical quantities, and can be misleading or deceptive. So that's kind of one of the downfalls of a pictograph, is that sometimes the artwork kind of takes the place of, really, a lot of the good math that's going on with the graphs.

Some of the benefits, though, of pictographs is that they are generally more pleasing to look at, and they also might draw in a reader that generally wouldn't look at a graph. So there are some benefits to pictographs as well. So let's take a look at an example of a pictograph.

What it's measuring is USA's largest national forests. And these are being measured in millions of acres. And then there are five of the top largest forests. So again, this is pretty visually appealing. They put it in this forest theme. It might draw the reader into it. But there are a couple things that I might have some issues with.

So for one, there's really no scale, so we can't really-- if we're measuring 16.6 versus 2.7, there's no scale here to measure it. So we aren't really quite sure if that's an appropriate measure-- that measurement there. The next thing-- where's 0? Is 0 at the bottom, or is that more like 1? We don't really have an idea of where this starts.

And then the other thing-- are we measuring the heights of those trees, or the area? So we can see, certainly, that Tongass, Alaska has, certainly, the largest bar-- in this case, a tree. But is it largest in terms of area? Are we doing it in terms of height?

For these, all of these-- these are pretty much straight across, so these are a more consistent area. This really goes to a point, so it's losing a lot of area. So are we measuring the heights of the trees, or are we measuring the areas here?

So those are just a couple things that might be a little misleading. Obviously we can tell that this is certainly the biggest, but there's not as much of a difference between these two. But again, are we measuring the heights or the areas? So that has been the tutorial on pictographs. Thanks for watching.