Scatterplots — Basic example

- [Instructor] Each year, a group of statisticians poll 1500 randomly selected United States adults with the question, "Are the Democratic "and Republican parties doing an adequate job, "or is a third major political party needed?" The scatterplot above shows the percentage of US adults polled between the years 2004 and 2014 that think that a third major political party is needed. Based on the line of best fit, the line of best fit, to the data shown, which of the following values is closest to the average yearly change, average yearly change, in the percentage of people that think a third major political party is necessary? All right, so let's see what they're, let's look at this chart here. And it tells us percentage of US adults that think a third major political party is necessary. And when you look at the actual, the actual plot right over here, the scatterplot, that in year zero, so this would be in 2004, it looks it's around, I don't know, 42% roughly. Then when we get to about 45% in 2005, this is year one, or one year since 2004. So this would be 2005. It keeps increasing all the way until we get to three years since 2004. So this is, or four years since 2000, actually, no, this is three years, since 2004. So this would be 2007, then it drops a little bit, then it increases, increases, drops a little bit, then it increases. But then they have this line of best fit, and this line of best fit, there's one way of think about it is the slope of this line of best fit is one way to think about the average yearly change in the percentage of people that think that a third major political party is necessary. Now, when you look at this, it looks like the slope of this line, it looks like it goes up, it looks like it's going up, I don't know, from this point, I'm just picking points that I can look clearly at the grid, from that point to this point. It's gone up. It's gone up 10%. It's gone up from 45 to 55%. So this has gone up, this has gone up 10%. And how many years did it take it to go up 10%? Well, let's see. It took it, it took it, let's see, this is year one, it goes up to year nine. It looks like it took approximately eight years. It took approximately eight years to go up approximately 10%. This is a positive 10%. On average, it looks like, if you look at the line of best fit, it looks like the, an increasing, every year that goes by, on average, more and more US adults think that a third major political party is necessary. This is of course the line of best fit. When you look at the actual scatterplot, it jumps around a little bit more. Sometimes it goes down or up, but if we look at the line of best fit, it is an increasing trend. So what's the slope of this right over here? Well, we increased 10%. We increased 10% in eight years, in eight years, so this is going to be equal, see, 10% in eight years is about 1.25, and this is an approximation, so let me put an approximation right over here. So approximately 1.25% per year, and it's clearly, it's clearly increasing. It's going from the bottom left to the top right. Now, let's look at our choices right over here. So we could immediately rule out the choices that have a declining, a decreasing, I mixed up decreasing and declining, a declining percentage. The percentage on the line of best fit, it's increasing. We have a positive slope. And I said it was approximately 1.25%. That's pretty close to this one right over here, and the reason why there is some not, there is some imprecision over here, is because I just I eyeballed it. I just eyeballed this chart right over here. I said, okay, this looks like it's about eight years. It actually could have been, it actually might have covered 10% in a little bit less than eight years, so there's a little imprecision over here. So these are all approximations, but even with the approximations, I got, I got very close. I got very close to this answer, much closer to this answer than I got to any of the other ones.