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## Statistics and probability

### Unit 2: Lesson 3

More on data displays# Misleading line graphs

Misleading Line Graphs. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- What is the easiest way to create a misleading graph?(105 votes)
- The easiest way to create a misleading graph is not to label the X and Y axes. If you leave off all numbers on the sides, then people will assume that two graphs have the same scale. Or that a graph (measuring one month that looks good) in a news story talking about something over a whole year will be assumed to be measuring the year in the story, not just a month.(172 votes)

- Is scale the easiest way to mislead a graph?(12 votes)
- Yes. Change the scale so that it seems one graph is worse.2:54(5 votes)

- Do we use misleading graphs in modern day life?(6 votes)
- You would be surprised how often they are used in politics, marketing, et cetera. https://www.youtube.com/watch?v=1F7gm_BG0iQ(2 votes)

- How can you tell what the exact answer is with graphs?(5 votes)
- Mostly the graphs are not used to tell you the exact numbers, they are used to show correlation between things or to show development of things in time.

If you want exact answers you mostly look for them in tables from which you have created graphs.(5 votes)

- Why would anyone want to draw a misleading line graph?(1 vote)
- 1. To mislead people. If people want to convince others, they can argument for their cause using data which not exactly support their cause, but look as if they did if presented in the 'right' way. They are not exactly lying about the facts in that case, but present them in a very biased way. For example when you want convince people of the benefits/downsides of a certain policy, the importance of some scientific results or the success of a buisness strategy. Or, in advertisement, to convince people of buying a product, Basically whenever it's about selling the data for some kind of benefit, this might happen.

2. Unintentionally. This might also happen unintentionally. If you present your data about, say a project to somebody, you choose a certain way to display it. This way you may choose because of convenience, because you want to emphasize a certain point or for any other reason without malintent. However, as you know your data very well, you might not recognize that you display your data in a misleading way, as for you all the information in it is obvious, whereas for other people, it is not and they will therefore more likely be misled by some aspects of the graph you choose.(7 votes)

- At4:03Sal said Thrill Cola but it's actually Thrill Soda(4 votes)
- who was the first person to think of the line graph?(2 votes)
- William Playfair was the first person to think of the line graph(3 votes)

- Why do people not completely evaluate a graph to make sure it is not misleading? Why does everyone like to see things go up?(3 votes)
- Misleading graphs may be created intentionally to hinder the proper interpretation of data to argue/convince the people about something that supports them or accidentally due to unfamiliarity with graphing software, misinterpretation of data, or because data cannot be accurately conveyed. Misleading graphs are often used in false advertising like the one Sal said in the video

Maybe because people are too lazy, I guess

Not just going up, it can go down too. Here's an example:

When people *glance*at a graph, they see that product A is rising and product B is falling and currently, A is better than B, which is not so they think that A is better than B, which supports the graph maker's favor.

Or when people glance at another graph, it shows that city A has lots of gunfights, which is not. The people think that city A is very violent, which is not which supports the graph maker's favor.

I hope this helps :)(1 vote)

- Are there any activities for misleading line graphs?(3 votes)
- It seems that Khan Academy doesn't have any activities for misleading graphs(1 vote)

- At4:25minutes into the video, Sal says, "how large 80% or even 70% is", what does he mean by this?(1 vote)
- Surveys such as this must have an adequate sample size and unbiased to have some sort of validity to them. So you could survey 10 of your close friends who happen to have a bias toward yummy cola, and come to the conclusion that 70% or 80% of them like Yummy Cola best, so 7 or 8 of 10 in a biased sample really is highly unreliable. Next, you go to a mall and do blind taste tests with 1000 random people, thus the results would be more reliable to say 70 or 80 percent prefer Yummy Cola unless you just happen to be in the town where Yummy Cola is produced (possibly biasing your sample). Next, you get a network together across the country and test 100,000 random people. This finally becomes an unbiased and more reliable survey when you say 70 or 80% like Yummy Cola better. So who is being surveyed and total number of people surveyed make a major difference on the reliability of the data. While this one is going down, the same would apply for the 16% or 20% for the soda that is increasing.(4 votes)

## Video transcript

Thrill Soda hired
a marketing company to help them promote their
brand against Yummy Cola. The company gathered
the following data about consumers'
preference of soda. So they have, year by year,
percentage of respondents who preferred Yummy Cola,
percentage of respondents who preferred Thrill
Cola, and then these are people who
had no preference. So in 2006, 80% liked Yummy,
only 12% liked Thrill, and 8% didn't like either one
or didn't have any preference. And so actually
just from here you see that many, many more
people liked Yummy Cola than Thrill Cola, actually
every year over year. So, Thrill Cola
definitely has something. They have an uphill battle. But then they said the
advertising company created the following two graphs
to promote Thrill Soda. And so let's see what's
happening over here. And let's think about whether
this is misleading or not. So if we look at this graph
over here, in 2006, sure enough, 80% liked Yummy Cola. Then in 2007, 76%. Then it keeps going to then
77%, then 73%, then 73% to 68%. So this is accurate data. It actually represents the data
that's given right over here. I'll do it in the same. It actually represents
this data very faithfully. Then right over here, if we
look at this chart, Percentage of People who Prefer Thrill
Soda, so over here in 2006, 12% preferred Thrill Soda. 2007, 19%. 2008, 19%. Then we go up to
20%, 21%, and 25%. So the graphs are
actually accurate. They're not lying. These are actually
the data points of the percentage who
prefer Thrill Soda. Now what's misleading
is if someone were to just look
at these two graphs without actually looking
at the scales over here, they'll see two things. They'll say, oh, look,
you see a declining trend. And that's what line graphs are
good for, for seeing trends. They say, look, I
see a declining trend in the percentage of people
who prefer Yummy Cola. And I see this increasing
trend in the percentage of people who
prefer Thrill Cola. And that's true. You have a declining trend here. And you have an
increasing trend here. But what's misleading
here is the way that they've plotted the scales. These scales are not the same. So when you look at
this, you say not only is there an increasing trend of
people who prefer Thrill Soda, but the way they
set up the scale, it looks like the
trend is above. The human brain is
tempted to compare these and to say, look, not only
is this an upward trend, but it's above this
trend right over here. Even in 2006, this
data point looks higher than these data
points right over here. But the reality
is that it's only because the scale is distorted. Now this is the oldest
trick in the book when plotting line graphs. It all depends on the scale. So this just looks good because
they used this scale that went from 0 to 30 as
opposed to 0 to 100. The better thing to do, or
the more genuine thing to do, or the more honest thing
to do, would have actually been to plot them
on the same graph. Although if they did
that, that wouldn't have painted a very good
picture for Thrill Soda. So if we plotted on the
same graph Thrill Soda, let's try that out. And actually, this
is even worse. You actually wouldn't
even be able to plot Thrill Soda on this graph
because they started this graph right over here at 50%. They didn't even start it at 0%. So you actually
would not even be able to plot Thrill
Soda on this graph. If you did, you would
have to extend this graph all the way down. So you would have to extend
this graph all the way down to-- so this would
have to be 40%. This would be 30%. This would be 20%. This would be 10%. And then down all the way
over here would be 0%. And then the Thrill Soda graph
would be all the way down here. So it was like 12%. And it goes all the
way up to like 25%. So the Thrill Soda, it
would have looked something like this. The graph would have
looked something like this, which
is nowhere near. If you plotted these on the
same scale, on the same graph, then it would have still
been pretty obvious that-- even though the trend
is downward-- a lot more people prefer Yummy
Cola to Thrill Cola. So there's two very disingenuous
things going on over here. One is the actual scale. For this amount of distance on
this scale, they represent 10%. So whatever the gain is, it
looks like it's a huge gain. And over here, on
that same amount, they're actually
representing a larger amount. They're representing
closer to 15% or 16%. And then the main thing is they
started the scale here at 50%. So they're not showing how
many people really prefer, how large 80% or
even 70% really is. And over here, they
start at 0% and they just have a larger scale. So it makes it look like out
the gate, a lot of people prefer, or a comparable amount
of people prefer, Thrill and that the trend is up. But the reality is still way
more people prefer Yummy Cola. So this was a little
bit-- or actually a very, very, not-so-honest
way of representing the data. Or I guess you could say they're
misrepresenting the data.