Hey there again, part two of in-class activity 4A. We're looking at mean and median. I had to stop for a minute. So let me share screen. We're wrapping it up and I have a terrible memory.
So we're going to be now using technology to um, to look at several groups. And at first they're going to want us to look at these. So poor sleep quality. So the bigger the score, I think it was poor sleep first.
Okay. Yep. Poor sleep. So I, because I want to save myself from flipping back and forth, I'm going to go ahead and I'm going to clean this up and I'm going to cut and paste it so that I can see it.
And then we'll do the technology. Would have been nice to have kept those red lines to see how good my estimate was. But too late now.
Okay. So I love this tool. Go ahead and move this. I'm all about the visual. So copy.
And I'm going to just put it, so we're answering problem number four, so I think I'll just plop it right here. It won't be perfect. Oh, that is pretty good, actually.
Let's make it a bit bigger. Okay, so there are distributions. Let's reenact them.
First, We're going to go to several groups. So I've got my, I've got my technology going, but I want several groups. This right now is set on single.
So I'll put it on several. And from the textbook, we want, we want sleep study, poor sleep quality score. So sleep study, poor sleep quality score.
So there we go. We can kind of see the data set down there. And later we'll do alcoholic drinks. But right now, this is our poor sleep quality score.
And I hope if we scroll, we'll see it. Oh, look at that. That's disappointing. It's box plot. But if I click the histogram there, yay, it's identical.
If it wasn't identical, I wouldn't panic because it has to probably do with the bin width. But I can see my picture down there and they're asking me to go ahead and fill in the means and the medians for poor sleep quality score, which is right here. So I can read that right off of here. And for the, now I have to be careful because it's listed slightly differently.
So they'll do LARC, they have LARCs first. So their mean for LARCs is 571. And the median for LARC is five. So this is porcelain quality.
The next one's the owls and that's $7.51. I'm looking right here on the screen to the right and no I got that wrong. Are we doing the owls next?
So it's actually five. Oh no, I was right, 751. That's so weird that it's almost the same number in reverse. And the median is eight, bigger and bigger. And then for neither, we have the mean of 602, 6.02. and the name is six so if i were to mark those on it's almost it so here we have five and so the owl is yellow and it's seven so i'm just gonna say it's so if i do the median it's eight so it's about right there i don't know if that's what it was you can go back and check the median for the lark is five that is a lot smaller and the median for neither is six.
So that's not six. This is maybe right about there. So, um, so I can see that in terms of poor sleep quality, if we look at the mean, the median, um, the higher the score, the worse it is. So, um, these guys are stuck.
are struggling. Brown face there. It's actually these guys that are struggling. Okay. So poor sleep is worse.
Okay. And, and also if you look at the means, it's the same, that is the largest and that is the largest. So there we go for looking at poor sleep.
Now let's look at alcoholic drinks. So I'm going to just go ahead and this is the alcoholic drink. So I'm going to go ahead and clean this up so we can mark it on there.
And I think I, so we'll have that to look at. I can't draw on that screen to the right. here. I'm going to paste image, make it a little bigger.
Okay. And now I'm going to come over here and the steps are the same. We're going to do several groups.
It's already there in several groups. And then we're going to do, we want to now this time have alcoholic drinks, sleep alcoholic drinks. I'm going to come down here, get rid of that one and do alcoholic drinks.
Let's see if I can find it. There we go. And it's still on histogram and I am happy to see that it's the same one.
And the more drinks you have, I think, well, oops, that wasn't good. Okay. Okay.
It is what it is. All right. So if I look here, First one listed to the right is the larks, the early birds, and the mean for the larks is six point, where does that move it down?
Oh I'm setting something off. Okay, well maybe screenshot it. I'm going to write it down.
Six, oh maybe that's why. um so 6.39 you guys can see it on your own and 4.59 and 5.57 and if you're reading if you're looking again at your screen because mine keeps disappearing so I got that information. Oh, that's so annoying.
That information right here. Okay. So again, I can see, and if I mark it, I think I'll do the medians again. So slice those cakes. So for the owls, it's seven, which is right here about.
And for. The LARCS, the median is three. That's quite low. The LARCS is three, maybe right about right here. And for the neither, it's five.
So it follows the same pattern, the largest median and the largest mean. So regardless of measure of center you choose, whether it's median or the mean, the owls have higher scores than both the larks and the nighters. And so how do the calculations relate to the comments and estimates you provided? For me, they were really close, pretty close. You may have had a different suspicion to begin with.
So answers are going to vary on that one. Did anything surprise you? Honestly, no. I thought that the owls, who I am a part of, are going to be more drinkers and more problems with sleep. So not me.
No. No surprises. I guess I was surprised that the larks for sleep quality are bimodal. That surprises me.
And also the owls seem to be somewhat bimodal. There's peaks, a whole chunk of people who do well and a whole chunk of people who suffer. I wasn't expecting that. I was expecting it to be more symmetrical.
reflect back on your interpretations, estimations, and calculations questions one through four. What might you conclude about the quality of sleep and drinking habits of those who identify as owls, larks, or neither? So I'm really, the thing that jumps out at me as an interesting thing is that regardless of measure or center you choose, the owls have the higher scores. So I'm going to write that down. Regardless of measure of center, you choose.
scores for both poor quality, poor sleep, and drinking, and increased average per week. Um, so there seems to be an association there. What is the same is the ranges are all the same.
Didn't really focus on that. Um, can I say that poor sleep might cause you to drink more or that drinking might cause you to have poor sleep? Well, I may suspect that, but I can't say causation. Let's say drinking cause poor sleep.
I'm going to put a big red no through that. Not right now. because it wasn't an experiment.
So it is an association. You cannot say causation, because we're just observing people self-reporting. So watch out for that.
That was from another part of the class, but it will show up on the midterm. So just a summary of notes here is there is a relationship. So median is the cut point. Mean is the balancing point.
And I do want to talk about data that is skewed. If the data has outliers or is skewed. So if we have the data, which way is it skewed if it looks like that? And which way is it skewed if it looks like that? Okay, so skewed is where the tail is.
So this is skewed right. And I want to draw a picture here. I'm always more confident about where the median is than the mean because cakes have a lot of meaning to me. So if this were a cake, I think I would say that that might be the median.
And the notation for mean. is X bar and it is going to be somewhere over here. That's the X bar. And why I know that is if I have a few high, got a few high outliers over here, this might be the housing market in Santa Barbara. where the median household house cost is still almost a million dollars.
But this might be Oprah's house and mine on one of these dots over here. So the median is about, I don't know, I'm guessing now, but let's say $900,000. and Oprah's house is 13 million. So if we do averages of all of our housing prices, Oprah's house is going to inflate the mean, which would be x-bar or mu. And we'll learn those, we'll learn that notation later.
X-bar is the sample mean. and mu is the population. What I want you to know for the exam is that the median is the better measure of center because this one is vulnerable.
This one gets pulled off of its center, literally pulled off of its center by the outliers. And similarly here, if I've got this distribution, the median, let's say it's about right here, where's x-bar going to be? x-bar is going to be over here somewhere, the mean. And this could be an example of your grades on your midterms.
Maybe you get two really good grades. But if you get one really low grade, one outlier, you bomb a test. We've all worried about that. It's an outlier.
So if you get an A, an A, and a flat F, you miss the exam or you got really sick, you average all those. You might be looking at a D average. Two A's and a flat F could actually pull you way down. that's not going to happen in this class because hopefully you're doing all of your homework and you're going to get decent scores on your homework and you'll be able to and you'll be doing quizzes and you'll be able to replace one of those exams because i don't want that to happen um so so here in this so this is skewed Those bad dogs. This is skewed left.
That's where the tail is. And so our outliers are over on the left here. And in this situation, you can be sure that the average, the mean compared to the median, you can be sure. This is going to be smaller, less than. the mean is going to be pulled to the smaller values because when you average it all a small outlier over here here the outlier deflates the mean so that's one situation this is another situation you So in this situation, up top, we've got our X bar.
How does X bar compare to the median? Who's bigger? Open mouth goes to X bar.
greater than. So here in when you have this kind of distribution you can be sure that the average of the mean is going to be bigger, gets inflated, and in this situation you can be sure that the average is going to be less than the median. So I think these pictures are pretty valuable and we'll put we'll be reviewing this again but for for now let's review what we went over in this class. Mean you know you add them all up and divide by the total. Median is the midpoint.
They are both measures of center. So we did that. You use them, they're numerical, and we've gone over how to use technology to find where the mean and the, I don't know why it's doing that. Sometimes it doesn't, sometimes it doesn't. So that's where the data falls, where you find it either with a single variable or one variable or two.
And you could do comparisons with the double variable and the double variable. is you locate it right here. And you can use the measures of centers to make grand sweet thing statements such as night people tend to be more likely to be drapers and night people tend to be likely to have not such good sleeping habits.
But you can't say that one causes the other. Okay, we are done. So take a little break and do the practice.
And I will see you in the next video. All right.