Main content
8th grade (Illustrative Mathematics)
Unit 6: Lesson 5
Lesson 6: The slope of a fitted lineScatter plot: smokers
Sal chooses the scatter plot that shows that smoking rate drops by 0.5 point each year. Created by Sal Khan.
Want to join the conversation?
This is hard is there an easier way to do this.??(4 votes)
Stick with it! You'll get it. What may help is to brush up on basic shapes of functions (ie: linear= straight line, logarithmic, exponential, polynomial, etc). These are taught in Pre-Calc and Calc classes already. A suggestion to Khan Academy might be to do a quick video and practice review section at the beginning of this section to review what linear/ non-linear functions look like in graph (non-scatter) form...and since I suggested it, I'll even do the video if you want me to, just show me the tools and code to upload the wmv. :-)(15 votes)
At 00:9, sal says linear association what does that mean?(5 votes)- The scatter plot looks like a linear function. It is almost a straight line.(12 votes)
At1:02, what does Sal mean by an outlier in the graph?(2 votes)
Something that doesn't fit in with the rest of the points(8 votes)
anyone from 2022 i understand perfectly(6 votes)- Wait so how would you just identify a linear or not linear if 2 look the same like graph 1 and graph 2.(2 votes)
- Graph 1 and graph 2 are both linear. You cannot identify them with linear association.
Instead, in the question, it said that percent drops by 0.5 point each year.
You have to compare two different points and figure it out.(4 votes)
why does khan academy exist(2 votes)- bc they wanna make money off us dumb kids(1 vote)
- At 00:9, sal says linear association what does that mean?(2 votes)
A linear association is when the points on the graph line up in just about a straight line, hence "linear."(1 vote)
I'm from India.
I also see some people smoking for a living. Really they should stop.
anyways, nice video! :)(2 votes)
At0:40, why does graph 3 has outliers?(2 votes)
One of the points doesn't fit in nicely when you draw a line close to the rest of the points.(1 vote)
Can anyone tell me the definition of outliers? I keep on seeing i on here and in class. Thanks!!(1 vote)- Outliers are numbers that 'stick out; among the rest.
1 2 50,000,000,000,000,000,000
^ A rather exaggerated example but it gets my point across ^^;
But more realistically, you would see
51, 52, 150
They're the huge numbers (or even small numbers) that stick out. They also mess you up when you calculate the mean, so be careful!
^-^(2 votes)
1:02Video transcript
The percent of adults
who smoke recorded every few years
since 1967 suggests a negative linear
association with no outliers. On average, the percent drops
by 0.5 points each year. Which of the following plots
suits the above description? So let's see, this looks like
a negative linear association. As the years go by, you have a
smaller percentage of smokers. This one does too. As years go by, you have
the number of smokers go down and down. This one down here
also looks like that, although it's not as smooth. If you were to fit
a line here, it looks like you have
a few outliers. Well, this is a
positive correlation. So we can definitely
rule out Graph 4. Now, the other
thing that they told us is that there
are no outliers, suggests a negative linear
association with no outliers. If you were to try to
fit a line to Graph 3, you could fit a line
pretty reasonably. That would go
someplace like that. But it would have this
outlier right over here. It looks like it's 12
or 13 years after 1967. So that would be 1980. It looks like an outlier there. But they said it didn't
have any outliers. So we would rule out Graph 3. And so we have to pick
between Graph 1 and Graph 2. So the other hint they give
us or piece of data they give us is that the percent
drops by 0.5% each year. So here's what's happening. In 1967, it looks like
we're at about 55%. And then 10 years go by. We are roughly at around
45, a little under 45%. So we dropped 10% in 10 years. That seems to be how much
this is dropping, roughly 10% in 10 years. Another 10 years go by. We go from 45, a little
more than 10% in 10 years. And so that would mean that
we're dropping, on average, more than one percentage
point per year. That seems more than
what's going on here. Now, let's look over here. Over here, we're starting,
it looks like, at around 42%. And then after 10 years,
it looks like we're at 37%. So it looks like
we've dropped about 5% in 10 years, which is
consistent with this. If you drop 5% in
10 years, that means you drop half a
percent per year. So we'll go with Graph 2.