Hi, welcome. We're going to do activity 1C today, and we're going to be discussing, initially we'll be discussing the salaries of professional NBA basketball players, but we're using this as a vehicle to understand measures of center. So in the last section, we did measures of spread, and we talked about standard deviation. We'll learn about...
other measures of spread later on. But today we're talking about measures of center. So the centers of our distribution.
So distribution is a picture of a variable. So in this case, the variable of interest is going to be MBA salaries. And the center is like, if we look at this cloud of data, this cloud of responses, where is the middle? And so there's different measures of center and they have different advantages and disadvantages.
So let's get started. I will share my screen. And yay. So here we go.
So a college basketball player is really great. And he or she. is good enough to make the NBA roster and is thinking about dropping out of college. So dropping out of college. So you probably, from a financial perspective, so I've underlined financial perspective.
So just thinking about money, not thinking about fun, thinking about money. Would you encourage this player to drop out of college? Explain. So of course, there's no right answer.
This is your opinion. So whatever you write is absolutely fine. So pause, write it down and come back to me. Okay, so I imagine that you fall into one of two camps. Half of you, or I don't know if it's half, but a good chunk of you are gonna say, don't drop out of college.
This- NBA career is only temporary. And even though you may earn a lot of money in a few years, you want to stay in college and college is so fun. So that's probably what you're thinking. I think the opposite opinion is yes, grab the money while you can.
And you can always go back to college later, which by the way, is not necessarily true. There's a window of opportunity when going to college is easier than other times. And we're headed. You know, we're sometimes we're headed for rough times financially as a country.
And the people who really get hurt are people who do not have college degrees. That's an undisputed fact. So what would I say?
You know, it really depends. It really depends on the situation. And the beauty of statistics is what I really so write down, you write down your opinion here. So you better write something down. What would I do?
What would you encourage the player? Would you encourage the player to drop out of college? I would not encourage the player to drop out, but I also wouldn't encourage the player to stay in.
I would say, let's look at the data. That's what I would say as a trained statistician. So if you scroll, oh, look at that. There's the data.
Now this is for Texas players and it's. this particular year, but let's just assume this is a good snapshot of all players. So it's a sample. It's not the population.
Well, if your whole interest is Texas, then this actually would be the population. So any numbers describing this, this data set would be parameters. But I think we're going to pretend, especially since we're in California or this class in California, that this is a snapshot of opportunities, that it's a good. representation. So before we get started, let's review median versus mean.
These are two measures of center. And the median has the letter I in it. Oops, that's not what I wanted to do.
The median has a letter I in it. And so median means middle point. And that means if you stacked up all of the numbers from smallest to biggest, the point right in the middle where 50% are so if we look here we stack them up median half are going to be on this side and half are going to be on this side so we just we're not paying attention to how much bigger or how much smaller they are it's just 50 50 so um i think about in terms of a cake if i cut the cake in half so that equal pieces on either side so um So that's median, middle. Mean, if you slide along, this is you hit the letter A. Mean means average.
So A for average, same as average. So you add them all up and divide by the total number. And the nice thing about mean is that it's really easy to calculate, especially when your parents took statistics. when computers had trouble a lot, we didn't have as much memory. Our computers were slow.
A mean, you just chuck all the information into, add it all up and divide. And that computationally is a lot easier. The, this, the medium is kind of laborious in that you have to actually order all of the data points from smallest to biggest.
And that may seem simple to you. but it actually creates, it's a lot more, you've got to have a faster, stronger computer to do it. So the mean average is a favorite for statisticians because computationally, it's not as hard to calculate. But there are some disadvantages to the mean. Specifically, it's weak.
We say weak, not resistant. to outliers. And so we're going to talk about or skewed data.
So you do not want to use the mean if your data is skewed or you have outliers, but you do want to use it if it's not because it's easier to calculate. So in some instances, the mean can be very misleading in some instances. In some instances, it's great.
So Means easier to calculate, but it comes with a little bit of baggage. And that's what we're going to be talking about today. So by the end of this section, I hope that you can identify misleading claims that can be made. Because there are a lot of misleading claims out there about mean versus median.
And we'll look into one of those today. So below is a dot plot of the NDA salary. So if I had, if one of my kids... So my kids are probably there in their early, mid-20s. If one of their friends was being recruited by the NBA, I'd say, well, let's look at the salaries.
And we're going to look at Texas ones just because we have them. And so here is the actual distribution. So there's a guy named James Harden who makes over $28 million.
So wow, that would have been a great decision for him to drop out of college for sure, because the money he can make. But what we notice, if you look carefully, here's a rookie, I think. I don't know much about basketball, to be honest.
But Chris Johnson only makes $25,000 a year. And he is right about here. And if you notice, there are people, there's a significant chunk of people in the Texas NBA who don't make.
any money at all, or almost no money. So a distribution salary, it's a picture where we've got our lowest value, and our highest value, and a value even higher. And the little dots show how many people actually have those those salaries.
So it's a picture. And what's disturbing is that while you think that the NBA people are you know, buying Porsches and living the fancy life. A lot, a good chunk of them aren't making any money at all.
Okay. So, um, describe the shape of this distribution and comment on any visible skew or outliers. Okay.
So pause and do that. All right. So for shape, um, for shape, What I see is I see this kind of a shape. so it's definitely skew when it has that kind of a hump in one place and it sweeps off in another that's skew and because the tail is over here which is the tail is on the right we say it's skewed right so you So skew isn't where, the question isn't where is the most data?
The question is, where is the tail? Where is the most unlikely values, the rare values? And that it kind of peters out.
So if it doesn't peter out, if there's just one dot, so that was kind of similar to the last in-class activity, the movie times for the G-rated movies. maybe wasn't skewed. They just had one rogue outlier, one, one movie, but here it's kind of petering.
It's petering out. That's what makes it be called skewed, right? So shape is skewed, right? And are there any visible? So the skew is definitely right.
We got that part. Um, but in terms of what are the outliers? Well, an outlier, I'm going to just go out on a limb. You haven't had a formal definition of outlier, but I'm going to say that James Harden's salary, Harden's salary of more than $25 million.
what's nice for him, is probably almost certainly an outlier. So what about this one? I'm not sure.
These are, so maybe I'll do a different color for those. We'll do a more washed out pink. We're not sure about these.
maybe outliers because I will be teaching you a test later on. But if they're, if they're petering out, but they're not significantly far from the pack, they might not be deemed as outliers. So the other salaries, Chris Paul's might also Chris. Paul's salary and others nearby might also be outliers. Visually, it's kicking off some red flags, but we'll learn more later.
But so whether you said one or four or even roped in a few more, the three after that possible, it's a good possibility. But we'll learn a more strategic test later on. Right now, we're just going for the intuition. So give an estimate of a typical salary.
So I haven't really given you a definition of what typical salary means yet. So I think it's important that we're able to look at the distribution in order to, what do you think is typical? Well, that's a good question.
What does typical mean there? Where are most of the salaries? That's what I would say. So I would say typical is right around here.
These look typical to me. So typical salary is anywhere between zero. And if this value is 5 million, then if that value is 5 million, then halfway in between is going to be 2.5 million.
So I'm going to say, so 2.5 million. 0.5 mil is right here. So this is my answer.
My answer is so focusing on typical. If we think typical means most likely, oops, sometimes I just can't write, most likely than the typical salary. is somewhere between, okay, zero, which is a bummer, zero dollars and two million. So between terrible and pretty fantastic. And 2.5 million.
So I'll do two, five, I think. this is million. So that's typical. So really, I mean, that's not going to help the poor guy who's trying to decide whether or not for finance, with the financial opportunity alone, he should drop out of college.
I am going to say most common salary is zero. And we'll just put a little throttle phase here. So warning, danger, danger to the guy. So maybe, but maybe he's extremely talented and knows he's going to end up being out of the chunk over here, in which case I would then say drop out of college if you want to without any problems.
Okay. So moving on. So we're going to now focus on median. So like I said, median, that's pretty green for that, median salary, they tell you, which is nice.
So they went ahead and they stacked up, what they did was they went zero, zero, zero, dot, dot, dot, and then two, two, eight, comma, two, nine, nine, three, nine, nine. They had all of the data points and they looked to the center where we have half of them and we have half the observations. Right in the middle is this value. I'm going to mark it. So try to estimate where you think.
This ends up being 1.6 million. So this is five, I'm going to just write this as this is 5 million. So we want 1.6 million.
So what I'm going to do is if that's five to draw, so why don't you pause it and try and estimate where you think it is, um, median first. So this value. Try to estimate where it is.
Okay. So I hope you paused it and tried. I'm going to chop this, this line from zero to five into five, into five pieces if I can.
So that's one, two, three, four, five. So I've got five chunks. So 1.6 is going to be a little bit between, so this is 1 million. And this is 2 million. So if I want 1.6 million, I'm going to just do a halfway point.
So maybe it's about right here, a little bit more than halfway. So I'm going to say this is 1.1 million, 577,320. that's what I'm guessing.
That's my process for trying to identify that. So and as you can see, if this were a cake, and you wanted to eat it, so I'm going to come back to this one. So I don't mess it up.
Maybe so it's about I said, that's 2.5. So what did I say? A little bit past that line.
So it's about right there. So if I would say this is half, that's half the cake. And then the other half is... over on this side. So it splits the region up into two equal halves.
So half and half, and that's the median that checks out visually for me. The mean salary, that's a good color for meaning. I want something very different than the red. I think the orange would be pretty good. So the mean is, 5 million, a little bit past 5 million.
So again, here's the 5 million mark. So where do you think that's going to be? Where do you think that mean is going to be? I'm going to say it's just a tiny bit more.
It'll be right there. 5.2. or 5.3 million so I'll just call this mean 5 comma 2 6 2 2 7 9 make sure to label the other one as median so huh do those look similar to you is there a big difference between 1.6 million and 5.3 million.
I'm rounding. So I've got my vertical lines. So I've done part A.
For part B, there are 61 players in the data set. So there are 61 Texas NBA players. Estimate the percentage of players who have salaries above above the mean.
Okay. So if we're going to do that, above the mean is going to be, so the mean is right here. So estimate the percentage of salaries that are above the mean. So above the mean. So it's going to be all of these values.
Those are all the values. So I don't even want to estimate. I want to be precise here.
Is I'm going to actually count them up. So we'll go ahead and circle them. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. So. there are 17, 17 players who have salaries above more than the mean.
So a little review on percentage. Percentage is always first. get the fraction.
So fraction is going to be part that you're interested over whole or total. So that's going to be, well, the whole, the whole is the 61 players. So we'll pop that down below.
And the part that we're interested in, part that we're interested in, is going to be all these guys. And we already counted that up as 17. So we'll pop that in. So that's our fraction.
So get out your beautiful, lovely calculator and do 17 divided by. 61. And you'll get a decimal and the decimal is going to be, and I'm going to round it. Oh, well, you get a horrible decimal, two, seven, eight, six, eight, eight, dot, dot, dot. I'll, I'll say on the midterm round, the default is going to be to round to three places past the decimal.
So we're going to round, um, to three places past the decimal. So that's going to end up being, um, around 0.27 and the 8th. is closer, eight, six is closer to nine. So if the, if the number sitting next is less is greater than or equal to five, you bounce up. So it's about equal to that.
And if I want to now do percent, then I move the decimal place two places. So it's about 27.9% or 28%. Did I, they did ask for an estimate.
So what you might have in directions, is, um, is, um, to answer as a whole. So that's about 28%. So a little bit more than a fourth of the salaries, um, make more than the mean. So would it be good to say that the mean is the typical? Well, I don't know.
Most people don't make above the mean. Um, okay. What percentage of salaries is above the median? So, um, I want you to be precise.
Use the red line that I've drawn. And if you go ahead and calculate, go ahead and count it off and see what you get and pause and come back. Okay. So what percentage is above the median?
So if you counted it, you're going to get, it's tricky to count. But if you want to do the percent that's above the median, you can go to all this. So it's going to be, you're counting up all of these dots.
And I think you're going to get between 30 and 31. And how do I know that? Because median is 50, 50. So by definition, you should get about 50%. Actually, you should get exactly 50%.
So. explain in simple terms okay so i'm going to say so i kind of tricked you by saying go ahead and count but it's good to verify it um because it's the mean the median We know almost or exactly 50% of the observations data points are above and below the median. So if you counted carefully, you should have gotten 30 or 31 if you did it correctly. But you could have cheated and just used the concept. Explain in simple terms why the answers for the mean and median are different in part B.
So here's the mean and here's the median. Why are they different? So what do you think? They're different because the data is skewed.
If the data is skewed, they're not going to be equal. And specifically, there are outliers that pull, what did I say, the medium comes from. adding okay so um mean mean comes from adding together all the observations and divide and then divided by the total number, by the total, the sample size, or population size, which in this case is 61. So if you have a huge value, huge values, huge unusual values will inflate the mean. So if we want to know how many people in Santa Barbara, what the average income is, well, you could add everybody's salary and Prince Harry and Oprah Winfrey, their salaries, maybe there are only two people who make these.
astronaut. We know it's more than that though. There's more than two people, but there's a few people who make a huge amount of money. And so it makes it look like we're all wealthy when we're not. So that's my explanation in simple terms of why the answers to the mean and the median are different.
So I'm just going to say the median is, it's not a calculation. is the middle. So whether that last value is almost the same as all the other values or is huge compared to the other values, that last value doesn't have a huge effect, doesn't have a huge effect on. the value of the medium.
It doesn't have any more of an effect than any of the other data points. So it's a fair way of assessing middle in a way. All right, so the next question, an MBA recruiter from for the Houston Rockets approaches a promising college basketball player.
And that recruiter says the typical come and join us. Have a good, it'll be fun, but you'll make lots of money. The typical Texas NBA player makes this much money per year, $5 million. Is this statement misleading? Why or why not?
So is this misleading? Why or why not? So when you're asked a question like this on an exam, please, it's a two-part question. One is make sure to clearly answer whether you think it's misleading or not, and then explain why. And the explanation is probably going to be worth way more than the yes, it's misleading, or the no, it's not.
So I'm going to, looking at this distribution here, and looking what that recruiter is doing, is that recruiter is using the meme. as if it is a typical salary, if it's common. And we already know that 25%, only about, well, 28% of people make more than that. So that's not everyone.
And in fact, if he's a rookie, he's probably more likely to be over here. So I'm going to say it's misleading. So this statement. is misleading.
So you can all, there's other, I wish that we were in class so we could compare different answers for why it's misleading. At this point, I can just give you my response, which is we already noticed, noticed that only about 28% of the Texas players earn more than that value, that value being the mean. And I would say, what did I say here? The mean comes from adding, the recruiter is using the mean, where he can say, he can defend his answer. Oh, well, that's one valid measure of center.
which, but I'm going to say as an educated person, which is inflated by a few outliers. So what's a better measure to describe this data set? If we're going to describe this data set, because this data set right here, is skewed, it's not actually appropriate to use the mean because we know it gets inflated by the unusual values in the tail. So I didn't ask you to say what he should use or she should use, but if the recruiter's being fair, they should use, at the very least, they should use the median. And even then that's a little dodgy because there are so many zeros.
Okay. I'm going to write that in even though it's not required because the data is skewed. It is more appropriate to use the movie. to describe the data set. Okay.
So that's a better. So when I ask you a question like this on an exam, it's your opportunity to show off what you know. So it's good for you to be working in the terms that you've been exposed to outlier, skewed, tail. mean and median, even though the question only asked about, you know, didn't even mention mean, but it's your opportunity to showcase what you know.
So especially if I say use statistical language to answer the question. Okay. For each of the following situations, predict and sketch the shape of the data and whether the mean or the median is higher.
So I'm going to use these symbols over here. Um, and if you want a video on inequalities, um, then, then let me know and I'll send you one. So if you see a symbol like this reading from left to right, this means, so if you read and read from left to right, which is how we in the West do. This means greater than.
And reading from left to right, this, if you see that, it means less than. So an example. five and seven well five is less than so that's the statement that reads as five is less than five is less than seven and there's lots of tricks to remember it open mouth to the bigger don't give him yellow teeth open mouth you to the bigger meal.
So it's like eating the seven instead of the five because he wants quantity rather than quality. So I have a whole video on that if you need it. All right.
So let's draw, let's think about the situation. So you're going to have to have knowledge to get this right. And I will try to always pick things that you, that I hope you know about. So you've got to have knowledge about income in Santa Barbara. You've got to have a sense of knowledge about GPAs at UCSB and you have to have a knowledge of people's body temperatures, which by the way, you could Google.
It's not cheating. So pause and just, we just want a general sketch. And then we want a statement about comparing the mean to the median.
Okay. So let's start with the sketches. Okay. So for Incoming Santa Barbara, and I'm just going to draw.
a straight line and the lowest income we could have is zero and there really isn't an upper bound on what the highest income would be so it just I'll just put a little arrow there and so I'm going to do some dots just so I think there are quite a lot of students in Santa Barbara and they don't make very much money at all all right so maybe we'll do I'm going to do 40,000 here And I probably should have done 50,000. So I'm going to make life easy on myself. I'm going to do 50,000 because I can add that better. So that would make this 100,000 right there.
So if that's 100,000, so that I'm going to do mimic. Here's 200,000. 300,000. So I think so. I've got a bunch of zeros over there.
I think that actually, contrary to what people think, there are actually a lot of working poor people in Santa Barbara, and you're poor if you make less than $50,000 as a family. I think that's a threshold for EOPS. If you want to qualify for EOPS, which is an amazing program. to support students.
It's called equal opportunity programs. And there's a couple of parameters that they look at to determine whether or not you qualify. One of them is whether or not your parents took and finished college.
And another is what your parents income is or your income, if you are independent, I suppose. So a lot of people. So these are little dots. So I'm just kind of getting. There's a lot of people in Santa Barbara, and I have no idea what the vertical scale is.
So I'm just going to think about percents. There's a lot of people who make less than $50,000. And then I think those are the people who clean the houses, work in the gas stations, go to school. And I think after that, there's probably a good chunk of people who make over $100,000. So I'm in this category as a teacher, but I don't make anywhere near $200,000.
But then, you know, there's Raytheon. So there's probably people all around here. And there's probably a few people in the middle range there.
And then we've got less people. So we've got, oops, don't want to do that. I think it starts to get less common, but there are people.
Wait, here's, maybe this is Oprah. I don't know how to spell Oprah. There's an H in there. And maybe this is Rob Lowe. He was on West Wing.
And I suspect Prince Harry is over here. So that arrow keeps going. And this distribution is definitely.
That's the shape of that distribution. And is that skewed right or is that skewed left? Answer the question.
It's good if you get it right. It's good if you get it wrong because you'll redo it in your head. This is skewed, definitely skewed. The tail is over here.
So it's skewed right. Skewed to the right. meaning there are some outliers, a few large outliers, a few people, only a few little dots over here, but those people make a whole lot of money. Okay. Similarly for, for GPAs.
So blue is a happy color. This way, and we'll start with zero, but it's not going to go to 300,000, 400,000. What's the biggest GPA you could have?
The biggest GPA you can have at UCSD is four. There is no five like there is in AP classes in high school. And so four is the max.
So it's a good idea to label GPA. I should have done that up here. Income.
income. So I'm going to label it GPA at UCSB. Well, UCSB is a world-class institution and the students who go to UCSB and you can transfer, we have a relationship with UCSB. The students who go there do very well and they go, they often go on to the graduate schools of their choice.
I am a product of the UC system. I was used to Santa Cruz. which actually is not as competitive as UCSB, I was still able to go straight into Stanford with a full ride for grad school because of the great reputation of the public school system.
So you can transfer into there. So a lot of people do well. So I'm gonna just, I'm gonna make little dots here that these are all people who've done fairly well.
So that's four, this is two, there's three. And I am just suspecting that whether you get a 3.5 or 4.0, it's pretty common. And then it gets less common after three.
I'm just guessing. And I think it's rare to get a GPA of one. But maybe there's one or two people and you really don't get a GPA of zero.
So. what's the shape of this distribution? There's the shape. And when you've got that swishing thing, where it's not a nice bell shape, we say that this, it's skewed for sure, but the tail is over here. The rare values, there's a few people who really bomb out.
So the tail is on. the left. So that means that it's skewed left. So skew has to do with where are the rare unusual values and do they kind of peter out? So it's skewed left in my brain.
You could look it up. Maybe I'm wrong, but that's what I'm guessing. And then the last one, body temperatures. If you look up, if you Google body temperatures, What you see, what you would see is that most people, what is the most common body temperature?
You're not too sick. It's 98.6, give or take. So most people, so these are rows and rows of dots. Most people fluctuate.
It looks kind of like this. And then you get. There there's some people who run cold and there are some people who run hot. So I'm right over here. This is me right there.
I tend to touch my, I tend to be cold all the time. I have a slow, low metabolism, probably because I don't exercise enough. My husband is over here. Tim is somewhere over there. He exercises every day.
He gets up in the morning, goes swimming, he does yoga. And then he makes sure to do a long walk in the evening. So he's really different than I am. The give or take is about, believe it or not, only about average mean is about 98.6. And the standard deviation, and I'm going to use sigma as D because it's of everybody, is about 0.6.
So this is the give or take. This means most people have a temp in Fahrenheit. So I should put this down here.
Body temp in Fahrenheit. Most people have a temperature of 98.6 degrees Fahrenheit. give or take 0.6 degrees Fahrenheit. So if we do that, that means that what's typical is anything between 98 degrees. And if I add six in the other direction, it's going to be 99.2.
So if you have a 99.2, you probably, you might not have a fever. It might just be that you run hot. So it's pretty stable distribution and that's what it looks like.
And what's that shape? That shape. is you've got a tail on either end, but because it's very balanced, this is not skewed.
This is symmetrical, and it's actually called, this is symmetrical, or bell-shaped. All bell-shaped distributions are symmetrical, but not all symmetrical distributions are bell-shaped. Symmetrical just means that you could draw a line right down the middle, and there would be a mirror image on either side. So in this weird case, since we have half on this side, go after that feature, we've got half on this side and half on this side. It's like a cake, and you cut it in half.
This is the medium. And if you added it because it's also all balanced, it's also and the mean. So this is the one beautiful situation.
Whenever you have symmetrical, adding it all up and dividing by the total number, you end up getting that the mean equals the median. Okay. So if you have symmetrical. All right.
So if you have skewed to the right, which is the first situation up here, well, is Oprah's salary, the outliers will inflate or deflate. And so the first thing I always do is where's the median. So for me, I'm going to go ahead and I will chop this.
if this is a birthday cake, the brown distribution, I'm going to say that half is on this side and half is on this side. I tried to cut it in half equally. So this is the median.
So it looks like the way I drew it, the median is below a hundred thousand, a little bit below a hundred thousand. And that makes sense. Half the people make less than a hundred thousand.
And half the people make more than 100,000 in Santa Barbara. So that's the median. So where do you think the mean is?
Do these data points right here, do they inflate or do they deflate the mean when you add them all up and divide? These are going to inflate. Outliers inflate. And that means the mean, I have no idea, but I'm going to guess that the mean is somewhere over here.
So the mean literally gets pulled off of its center, pulled to the outliers. So in this situation, the mean, if I want to compare the mean and the median versus median. Who's bigger? Well, the mean is over here.
And it looks like if I'm reading it, it looks like it would be about $250,000. If I look at that scale that I made, that's the mean. And the median is below a hundred thousand.
So the median, I'm going to put the open mouth to this one is bigger. And if you're worried about the symbols, you can just write in words, the mean. is bigger than the median.
So for that one, the huge outliers inflate. Here, we've got a few students who did really badly. Those are the outliers. And in this situation, so if I do the birthday cake thing, I know that the median, if I look here, it looks like it's, oops.
where does it do that it looks like the median maybe is about right here it's about 50 50 actually that i'm going to move it over a little bit maybe it's about right here writing come on baby write for me it's weird i'm going to say that's the medium it's always easier for me to visualize the median And then the few outliers over here. are going to pull the mean lower. So the mean gets pulled off the center by these, you add them all up and you divide.
Well, you know, that experience, if you had, you do well on two tests and then you bomb a test, like you get an A and a B, and then you miss or bomb the last test, you're going to, you could even have a C average. It could devastate your grade, right? Not in this class because you can replace them.
low score with your final exams. So that's okay. But in this situation, the mean compared to the median, who's bigger?
Well, if the mean, the mean is over here on the left, it's smaller. So, and the way that reads is the mean is smaller than the median because it got deflated by these bad boys over here. Not that they're It's the grades are bad boys. They're just bad, bad grades, I should say. And then we already have, so we've got these situations, this situation, this situation, and this situation.
Okay. And that's it for this. So in general, for summary, if you have, this is skewed to the left, this is skewed to the right.
and this is symmetrical. Always the mean is greater than the median in this situation. Always the mean is less than the median in this situation and always the mean is about equal to the median in this situation. And the only time that you really should use the mean should or can can use me as center because there are no outliers okay So that one for these two should use median as measure center because we say it's robust, strong, or resistant. to outliers.
Okay, so the summary, we come back up here, the summary here, median is resistant to skewed and outliers, so we covered that. The mean is not resistant, we covered that, and in some situations, specifically when the data is skewed, you should not use the mean to describe the data set, you should be using the medium. That's that one.
And so don't be manipulated by the media. If they're saying that the mean people who are going to get their tax returns and get more than, you know, $500 back for taxes is inflated, it's possible that you're not going to get anything back for taxes. Okay, thank you.
And take a little pause and do the practice. Okay, recording. Where is it?