Transcription
SAL: I'm here with our exercise guru, Ben Eater.
BEN EATER: Thanks, Sal.
SAL: And we're looking at your exploring standard deviation 1 exercise. And let me think about what's going on here. It says, arrange the 13 orange sample points in the histogram below. So these are the orange points you're talking about. So the sample standard deviation is approximately 1.6. So just so I understand these, these are points that are being sampled from some distribution?
BEN EATER: Right.
SAL: We get these points right over here. And then your module is automatically calculating the sample mean.
BEN EATER: Right.
SAL: Which is kind of the central tendency of at least these points. It's estimating the mean of this population you're sampling from. And then also the sample standard deviation, which is really kind of a way to measure, on average, how far away they are from that sample mean.
BEN EATER: Yeah, and what we're trying to do here is to kind of get a sense of what that actually means. So we say the standard deviation is 1.9, what does that sort of feel like?
SAL: Right. It seems clear that the sample mean, it looks like it literally is the average of these numbers.
BEN EATER: Right, it is.
SAL: And it looks like if I move this out, then it moves to the right a little bit. But that's just one point. The mean moves to the right. The mean, I think, it's easier to have an intuition for the mean.
BEN EATER: A lot of people have a pretty good sense of it here.
SAL: If stuff moves to the right, then the mean moves to the right. If we move stuff to the left, then the mean moves to the left. That makes sense. But the standard deviation in this case, we're measuring the sample standard deviation. This is a measure of dispersion. And I say "on average" in quotes because it's not exactly the on average that we typically--
BEN EATER: And that's kind of the point of this exercise. It's not kind of exactly on average, so what is it?
SAL: Right. But you see that the further-- so let's see, the further the points are spread out, the wider this sample standard deviation is. If I bring the points closer together, then the standard deviation gets smaller and smaller. If I bring them closer to the sample mean, as you see, they get tighter and tighter. So let's see, let's do the actual exercise. So arrange the 13 order sample points so the sample standard deviation is approximately 1.6. Right now it's 2.1, so I want to squeeze things together. And there's no right answer here. I just have to get them in a way that I'm close to 1.6. So I want to move things closer to the sample mean. And so let's see this one, so 1 point by itself-- actually just moving this 1 point--
BEN EATER: Not quite.
SAL: Just that 1 point didn't quite do the trick. But I could move more things in. And it really could be I could pick another point, move it closer to the--
BEN EATER: Lots of ways to do it.
SAL: I'll have a bigger impact if I move something that's right now far away and move that closer in.
BEN EATER: That's right.
SAL: Because right now that's kind of taking that-- OK, that looks right. 1.6, so let me check my answer, correct.
BEN EATER: Now, look at this show solution.
SAL: OK, show solution. The standard deviation is smaller if the points are closer to the mean, yes. The standard deviation is larger if the points are more spread out. Try removing a point closer to and further away from the sample mean to see how the sample standard deviation.
BEN EATER: So that's telling us what we just did. Look at the next step.
SAL: Oh, there's another step.
BEN EATER: And what this will do is actually show you different examples of how to get to 1.6. So if you click that, it'll show you maybe a different way.
SAL: Oh, that's neat.
BEN EATER: Now, click it again. And so what you can see is there's lots of different ways to have a sample standard deviation of 1.6. And they may look different, but if you keep clicking that, you'll kind of see there are some things in common as far as how they are grouped close to the mean.
SAL: And one of the things I just want to clarify is you've drawn this kind of bell curve with that area shaded in the back. That is our estimate of what the real distribution might look like based on the information we have of the sample. So if our sample mean is accurate, if it really is estimating the true mean of this population, then that's what we're drawing in the middle. And then we're assuming it's a normal, just kind of bell curve shape distribution. So that's what it would look like based on information we have.
BEN EATER: Right.
SAL: This is very cool.