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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.

## 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.