Hey there, welcome back. In class activity 4A, it's called feeling sleepy exclamation point. So we're going to look at data from an earlier section 3.A. And I don't know if you remember identifying yourself as a lark or an owl. If you're a lark, then you tend to get up super early.
And if you were an owl... You tend to want to stay up super late at night. I'm definitely an owl, something I should probably work on. And then you could be a neither.
So now we're going to look at that data again. And we're going to be looking at more. Let's see if we can get it. We're going to be looking at groups of people who fit. So are you an owl?
stay up late? Or are you a lark? Get up really early? Or are you a neither? You're just kind of middle of the road.
Or you don't have a preference. So people can fall into one. Oh, by the way, I, my dog head butted me.
That's why I've got a big bandage on my face. So right now, if you could make some. guesses, how might the quality of sleep differ among these groups? Does one group tend to sleep better than the other? What's your suspicion?
So quality of sleep, how does it differ between the groups? And then the other question is, do you think that one of the groups consumes more alcohol than the other? Um, that is an interesting question. So what's your suspicion?
Why don't you write down your thoughts, um, right here? Okay. And there, there's no wrong answers. It's just what you think.
All right. So what do I think? I am an owl.
So I hope I don't offend anyone when I say, I think that it's probably. likely that the owls might be less disciplined. So Bronwyn guesses owls are less, let's say structured.
So they might not be rule followers. So more likely. to not be rule followers.
So she thinks, she being me, they might drink more. That's just what I think. What do I know?
I'm just... I'm not a social scientist. I don't know.
So that's my comment on drinking. And then sleep quality. I also think up late means not as good as good sleepers.
And there is actually a lot of data to show that you sleep better at night if you're exposed to sunshine. during the day, particularly in the early hour morning. So I'm going to go out on a limb and say that I think that owls not as disciplined drink more, sleep less, have trouble sleeping.
That's my guess. We all have different guesses. All right. So we're going to use this as a vehicle to understand mean, mean. and median.
Okay. Those are both measures of center. They're both measures of center.
They're a little bit different, and we'll talk about the differences and the strengths and weaknesses of both. And that's the big, big new thing. And we're going to use technology.
So we're going to calculate the mean and the median using technology, yay technology. And once we have that, we're going to do comparisons. of different groups. So that's what we're doing today and we'll make connections between which measure of center happens due to the different graphical displays.
So certain types of graphs lend themselves to having one measure over the other and some measures will indicate things about graphs. And we'll get to that. Okay so before we get started Let's refresh our memories on two of the variables, two of the characteristics that came out of that sleep study from a couple of sections ago.
So we have poor, and I do want to pick the same. We have poor. I'm hoping I'm picking the same colors.
I'm just going to flip ahead for a second. Look at the colors. Okay. So poor sleep quality, sleep quality is green.
Okay. So we have poor sleep quality scores. And what's important to note is that worse scores, greater number means worse quality. So it might be a little counterintuitive, but the bigger the number, the more trouble you have sleeping.
So people were asked. And it looks like the scale is even beyond 10. So zero to 11, maybe, I'm guessing. And then the other thing is alcohol drinks. So how much alcohol do you consume a week? And that's just the more, the bigger the number, the more you drink per week.
And it's going to actually be the average. per week. So average number of alcoholic drinks consumed per week. So those are the variables we're going to look at first.
And here is, if you go to our lovely website, here are two histograms to describe the poor sleep quality and the number of drinks. And they are stacked histograms. So I do notice that the counts This is count and this is going to be sleep quality number of students who have certain sleep quality scores and this is also count but this is going to be number of drinks. No, it's not. It's going to be number of students still.
It's all number of students and the variable of interest for this one is going to be number of drinks. But if we go up here, it's going to be sleep score. So I like to label my horizontal axis so that I can really, so if it falls in a certain place. So if I come out here, if I come out here and look at this one right here, it looks like there might be one.
The sleep score is terrible. And I looked it up. It's actually 10.3. And there's one student who rated their sleep scores at 10.3.
So their sleep was so awful, it was maybe beyond the scale. And I'm going to go out of my way and say that's an outlier. So there's one student who has a terrible sleep score. And then over here, student with terrible.
sleep score so maybe that student works a night shift maybe they have a roommate who's torturing them who knows something's going on there and then if we look again let's look at some outliers over here um if i look at the scale along the side here it's slightly different those scales are different but the scale on the horizontal axis is the same so here the bin width i already checked is two. So I'm going to guess this is 18 and this is 20, 18, 19, 20. I'm just guessing because we can't hover. But let's say it's somewhere between 18 and 20. So what that tells us, the height is maybe around two. So I'm going to say the height is two students. drink an average of alcoholic drinks between 18 and 20 drinks per week.
Yikes! And then there's another one. One student drinks around 24 drinks.
per week. So we're just getting used to the distribution. And if you come over here, there are, it looks like there's over 30 students who don't drink any drinks at all.
And that's what this column is telling us. 30, let's say 32, I'm guessing 32 students. Don't drink.
Okay, so I've got a sense of my histograms. So now they want us to go to describing, go to the quantitative, pick a single, the single group tab, and we're going to be using data from the textbook. And we're going to pick sleep study, study score, the core scores. So we're going to be looking at this one first.
And then second, we'll be looking at the alcohol sleep one first. And then we'll look at the alcohol after. Okay, determine the mean and the medium.
So I'm going to get the mean for sleep study, mean for sleep score, and I'm going to get the medium. And then when I'm done with that, I'm going to get the mean and the medium for alcohol and drinks. All right, so let's do it.
So number one, I've got to find my, if I hit that tab, I should get this one. quantitative area and you should get this and then from the textbook it says single group single group which is the default so i'll leave it there and from the textbook i'm going to first do the green so textbook Not average sleep, but poor quality score. So I've got to find that one. There we go.
And the default bandwidth is two, which I think is fine. And if I now go here, I can see, if I look here, it gives me the mean and the median. So the mean is 6.26. and the median is six. Now which one is easier for me to visualize is the median.
And what we learned prior is the median is what will cut it into two equal parts. So I'm going to write that in the notes here. So this is summary of notes.
Summary of notes. median cuts the distribution as if it were a cake into two equal pieces. Okay, that's different than the mean. I could call it for mean. Mean is the balancing point.
So you want to think of if you were going to balance your distribution on your finger and it's top heavy, where are you going to move it so that it doesn't tilt? That's just a conceptual. So let's go back and mark these on the picture. So if I do the mean, I'm going to do the median first because that's my favorite.
to six so if i look here six is maybe right about here does that look like this is half and half sure it does right we've got six here so six is that cut point and the mean is just a little bit off to the other so just a tiny bit off So maybe this is the mean. So that's if it were a seesaw, you don't want to put it so it's half and half because you've got these values. You've got outliers over here.
So to balance the weight of those outliers way over here, you're going to your means going to be not actually so that it's splitting it 50 50. It's a tiny bit the other direction. So. now let's do it again.
So now we're going to do it for the drinks. So we'll go up here, switch it to and I really hope you are doing this with me. So now we're doing it alcoholic drinks. So there it is.
And I'm going to move it so that I'm going to keep the bin with two so that I can really stack. them and the distribution looks a little different do you see that and I imagine it's because the bin widths are different so that can make your distribution look different but the 25 is still out there and I actually I'm going to hover on this one now and let's see what it is so one person drinks between 24 and 25 drinks per week which is quite a lot if you're a student And then there's nobody who drinks between 22 and 24. But then there's two, there's a kick up. But how many students don't drink at all? Maybe about 42 drink one or two drinks. So it's a little bit different, but there it is.
There's your histogram. Looks a little different because the bin widths are different, but it's still a good picture. And if I look here, I can see the mean and the median.
So if you look there, the mean is 5.57. That's our balancing point. And the median is 5. So I'll go over.
So the median, is that going to cut your distribution into two equal pieces? I believe them. Why not?
And then again, it has those outliers that make your balancing point a little bit more. You've got to kind of deal with the kid. If it were a seesaw and you had a kid way off to one side, you'd have to try to move that so that it...
it can balance. So there we go. All right. In a few sentences, interpret your findings. So for C, there can be lots of different answers here.
And I notice that particularly people who are used to having the kind of the short answers, if I give you just an open space like this, sometimes you're in the headlight. So you want to state the obvious. So I'm just going to, I'm literally going to state the obvious here.
The median for sleep score is six. This means, that's an unfortunate choice of words. I'm going to say indicates instead of means. This indicates, it demonstrates, indicates that half the students have a score better than six. which means less, and half have a score worse.
Okay, so that's what the median tells us. Average, the mean, is slightly more. Well, if you average a whole bunch of normal scores and then you average the outlier, the average gets inflated, inflated by the outliers ever so slightly, ever so slightly. So that's, that's my observation about the median and the mean for. for the sleep score and I could write a very similar one for the drinks.
For number of drinks or drink average, and it's kind of confusing because each observation is itself an average, the meaning is What did we say? Five. That's actually pretty good, I think. Meaning, which is demonstrating that half the students drank. less than average of five flanks per week, just like the green distribution, other distribution.
The meme is ever so slightly inflated or increased, blown up by some outliers. So I think that's all they wanted. A few sentences, interpret your findings. So the findings are about the mean and the median. So I would say these students are better than the students that I went to college with, that's for sure.
An average of five drinks is fantastic. There are a few students who definitely have some developing problems. And I'm worried about them, even these.
And so there are, it trails off a bit, but for the most part, I think this group of students is doing pretty well. And their sleep score, well, if it's out of 10, their sleep score is a little high. So these students are having trouble maybe with sleeping, a significant number of them. Okay, that was just mine. Now, so now the colors mean something entirely different here.
Now let's compare the sleep quality. and alcohol consumption habits between those who identified as owls, larks, and now let's compare the sleep quality and alcohol. Okay, so we're doing sleep quality here.
These are all sleep quality, and what we're dealing with is larks, owls, and neither, and to see if there's any difference. And so they've already made the histograms for us. And I wish that they would put, they would say count, count, and count. So it looks like we're dealing with counts. So we're counting students again.
How many students fit in each category? So what do you notice about these histograms? Based on their estimated mean and medians, based on their estimated means, did they ask you to do that?
I'm drawing a histogram, so it's a whole different histogram. Does it appear that one group has worse sleep quality than the other group? Remember, bigger score.
Bigger doesn't mean better in this case. greater score, worse sleep quality. So which of these groups has more bigger scores?
That's what we want to ask ourselves. So if I chop, I want to see if I look at the larks and I'm just going to estimate, I really like medium. So I'm going to use this pretty color for mediums and I'm just going to estimate what the median is. So I'm looking at the green.
distribution and I'm thinking about a key line pie and I'm saying if this is a key line pie and I want to cut it and share it with my best friend I'm going to cut it right about there it's a straight line so let me try again I'm going to cut it right about there and I'm going to get this half and she's going to get this half and that is the median that's what I'm guessing And so it looks like half the scores are quite low. If I look at this, if I look at this group over here, if I look at this group over here, that is on the low range. So that's a good thing. So that means that the larks are getting some good sleep.
If I did the same thing for the owls. So here now I don't have a key lime pie. I have a, let's see, what would I call that? Maybe it's a cheesecake or a vanilla pie.
If I want to do 50-50, I think it's going to be about right here. I'm just eyeballing it, but something like that. And it seems like I've got a lot more of the supposedly... bad scores. See that I've got the bad scores, more bad scores here, bad scores.
There's almost nothing like that. If we look here, there's almost there's nothing there for that. So I'm going to say that the owls are definitely struggling more than the larks are. Now let's see the other people, the people who are now.
So if I, in fact, if I draw that line, if I keep drawing that line, which is the halfway point for the yellow distribution, almost none, no scores, very few people. in the Lark category have scores that high and the same is true, almost none. So, um, I would say, unfortunately I was right that the Larks, my group of people do not sleep as well, probably because they're up when there's no sun. So I'm going to go ahead and write that.
How do I write that up? What do you notice about these histograms based on? their estimated means and median. So I'm using the medians.
So I'm going to just own that. Looking at the median estimate for owls, I see Almost no larks or neither's have scores as high as half the larks. The larks are suffering with poor sleep at a higher than the others.
That's just my, that's my take on it. And similarly, if you, the other way, you could say the same thing about the larks. You draw, here's the median right here, and there's almost, well, there is actually a good chunk of people, about a third, maybe a third of people in the, in the larks, in the owls, sleep as well as half.
So it's not as alarming as if you focus on the low scores. I mean, the bad scores. The bad scores pretty much reveal that the larks, the owls have a good chunk of people suffering. So that's that.
Now let's switch gears. Instead of poor sleep quality, let's look at alcohol. And again, we've got these stacked, so we're counting students. And we want to compare the two in terms of who's drinking more.
Well, I see a lot of larks with very low drinking scores. There is a fair amount, but it's not the same. But the LARPs and the and the Nithers seem to have these seem similar. This seems smaller. This seems like a smaller chunk to me.
So and notice the count here is different. A lot more people said that they were neither. So that's an even greater number of people. But proportionally speaking, I would say this chunk right here, this chunk is very similar to this chunk, but it's smaller than that chunk. So if we look over on this side.
the larks are not drinking very much. There's someone with a drinking problem, but as a trend, the larks, this isn't hardly anybody, almost no students here. But if I look at that same thing, that's a bigger chunk. And that's there.
I would say that the larks and the niders are pretty similar. in that there's definitely a tapering off of drinking as you go out. So how could you see that?
So we're not really looking at medians here. If you look at the shape, though, if we do shape instead, that is definitely tapering off. And this is tapering off not as extremely because we've got this.
outlier here that messed that up, but similar trend. I would say this one, if you ignore, so there are a lot of owls that seem to drink very little, but if you go far out from there, it seems a little more uniform. So one way or another, these guys are drinking more, more students drinking more. Okay, so I can see that.
So the owls seem to be the drinkers, though there are exceptions in all groups. Okay, so what did they ask here? So I was just looking around, just playing around with that. Following the histograms illustrated, illustrate the distributions of the drinkers, how the drinking habits.
Okay, what do you notice about these histograms based on their estimated? So what I notice is overall, The larks and nithers are more similar than owls who have more drinkers. It's more common to have drinkers taper quite a bit, not as much, not as much. Okay, that's overall. But they do ask us to think about the medians and the means.
So if I drew a line on these to cut it in the half, And do they actually ask us to find the mean and the median? I mean we can. Did they ask us to? For number 4b, what do you notice about the histograms based on your these estimated means and medians?
I'm looking right here. Based on the estimated means and medians, does it appear that one group consumes more alcohol? So I wasn't really, I was just looking at the overall shapes.
But if I do the means and medians, and again, my favorite is the median. If I cut this cake in half, it's going to be somewhere around here. That's going to be the median. Just guessing.
This cake is going to be somewhere around here. And this cake, just eyeballing it, is going to be somewhere around here. So the median for the owl.
is greater. Estimated median for owls is greater than the others. That's just what I'm seeing.
So now we'll go see if how right I was about that. So go to our cut and paste this, we're going to go to several groups. So we're going to look at everything all at once.
And we're going to use a textbook. And we're going to do sleep study for quality of sleep. And then we're going to do alcohol to determine what the actual mean and medians are. So, and we'll do it on the next page.
So we're going to record this here. So I'm going to go. Actually, I think I'm going to pause here. And I'm going to want you to try to do this and then come back and fill this in. Okay, and so this will be a part two.