Friday, May 20, 2022

90% of People Don’t Understand: Mean vs. Median

Okay let's talk about the words mean and median and we're talking about mathematics here and uh these words are uh pretty common and uh you know kind of our everyday vernacular you see them all over the news and especially financial news and whatnot they're all still talking about the mean or they're talking about the .

Medium but guess what in my experience like 90 percent of people don't really understand these terms oftentimes they are confusing the two all right and they're really thinking uh probably most people are really thinking about the mean when they hear the word median and uh you know when you do that .

You are completely misunderstanding the description of what's going on when someone is saying the medium they mean something completely different than the mean okay and so what we want to do is clear up any confusion with this and if you're confused then listen uh there's a lot of people that are confused you know these are terms of course for me i'm a .

Math guy i work with uh mathematics all the time so of course i'm gonna know this uh so you don't feel bad if you're confused about this but let's get you uh squared away on the mean versus the median basic uh statistical concepts but very very uh common words all right if uh in terms of you know just watching the news or you know reading anything uh .

These days you know especially economic uh about the economy or economics or you know business and stuff you're going to see these words and we want to make sure you understand the difference between them and what they mean okay so we're going to get to this in just one second but first let me quickly introduce myself my name is john i'm the founder .

Of tablet class math i'm also a middle and high school math teacher and over several years i've constructed what i like to believe is one of the best online math help programs there is of course i'll let you be the judge of that bold statement you can check out my math help program by following the link in the description of this video but uh .

Basically i have 100 plus different math courses super comprehensive math courses not little quick tutorials when i teach i try to get my students to truly master you know the concepts and quick little tutorial videos that's okay for like an overview but that's not what i do all right i try to get my students to really be the best but um .

My courses range from pre-algebra algebra 1 geometry algebra ii going to be launching precalculus here shortly but i also do a lot in area of test preparation so if you're studying for like the ged sat a-c-t gre gmat asvab accuplacer alex exam clip exam teacher certification exam any of those exams and many others .

Just go to my website and check out my full course catalog and guess what all those exams have a good amount of math on them if you don't do well on the math section on those exams you do not do well on the exam so i can definitely help you out if i don't have the exam that you're studying for drop me a line and i'll .

Help you out the best i can anyways now i also do a lot with independent learners like homeschoolers i've been working with homeschoolers for 15 plus years so i have a great home homeschool learning system so you might want to check that out then i just help those who as well that are just struggling in your current math course .

Now if you're truly serious about wanting to learn math or improve in mathematics then you got to be serious about this and that is note-taking all right so you got to take great math notes don't blow this off this is absolute must and it's an everyday discipline okay if you do this okay i'm going to tell .

You over decades of teaching mathematics you are going to do very very well right this is just the kind of the rule of thumb that i've seen and then the reverse is true if you are more into your cell phone talking to your friends and kind of like you know doing homework in another class during math class guess .

What you're gonna you're probably not gonna like your final grade all right and you can't be saying my teacher is the worst i don't like that teacher listen you gotta take uh personal responsibility and um you know look at your notes that's going to tell you whether you are focused and .

Engaged uh the thing about anything that you want to learn okay is focus focus is the key and you need an activity to you know keep you away from all these temptations and distractions that's note-taking so every day you go into math class be like all right i'm going to take some awesome notes and if .

You have that attitude and that discipline you're going to do very well but in the meantime you probably missed a bunch of material so i um offer detailed comprehensive math notes to include pre-algebra algebra and geometry algebra 2 trigonometry you can find the links to those notes in the description of this video as well okay let's talk .

About mean versus median if you think you understand the difference well let's let's uh see if you do so here's some numbers this is what we would call some raw data all right just a status set okay so it's 2 9 3 1 and five and uh i'd like you to calculate the mean and median please do .

Not go look at your notes don't google this real quick and just see what you know see what you remember right the mean and median you could use your calculator if you feel like you need to but really it's really super easy stuff you don't even need your calculator and uh i think i'll give you all of about 45 seconds in order to determine uh the .

Correct answers here okay all right so if you don't want to see the solutions yet pause the video because i'm going to go ahead and answer this now but this is just a little pop quiz all right let's just determine do you understand the mean and meeting right now okay so here we go .

And let's start off with the mean all right this is the mean what is the mean okay well let's just answer this right now the mean is the average that is what we're talking about so when you're asked to calculate the mean uh we are asked to calculate the average so how do we do that well here's our data set we're going to add up the numbers we .

Have one two three four five we're going to add them all up and how many numbers again do we have one two three four five we divide by how many numbers we have so we add all these guys up divide by five and we will get the average or the mean all right so this when we add up all these numbers you should get 20 and we have five numbers so 20 divided by five .

Is four that is the mean and if you got that right well then let me give you a little happy face and a check mark that was pretty easy but guess what you know uh it's shown me that you have an idea of what these uh basic statistical terms mean .

All right now let's get to the median all right let's get to the median so what is the median well first things first here is our data set okay it was given to us 29315. now you can see i have the answer here the answer is a fact three but this word median doesn't kind of sound like the word uh like .

Middle all right like median middle maybe there's something kind of kind of related here well in fact there is the median is the middle number okay it's the middle value but we have to order our uh data we have to put it in uh lowest to highest order first to determine that i can't just go like right here well in .

This case you know let's just kind of mess around here let me put the one let me put the three like this oh okay it's the middle number so uh this is in the middle um same data set here by the way so one is the median wrong wrong answer okay that's not the case we have to order .

From lowest to highest first we go one two three five and nine and now whatever is the middle value okay is the median right that means that what exactly half of the values in your data are less than the median and half are .

Higher than the median okay now let's talk about so 3 is the correct answer and if you've got that right if you got both of these right then i must give you a happy face with a little mohawk an a plus and a 100 that's very very good but let's talk about how we see this stuff in uh .

Financial news and things like that it's very common so they'll talk about like let's talk about like median home price uh this is pretty common let's say that's like in a particular area 350 yeah home everything is getting so expensive these days .

Uh homes gas food yeah we truly do have inflation going on but let's talk about median home price what does that mean right so let's say you live in a particular city all right city y whatever the case is so here is the city right here .

And uh the median home price is 350 000. so here is our lovely little home in our city so if that's saying well the median home price what's that say well it says that half the houses over here are going to be less than 350 000. okay well 350 000 i could do better than that 350 000 okay half are going to be less and then .

Half are going to be more okay exactly one half are going to be greater than 350 000. that's what that under that's what that means okay the median home price so that gives you a sense right off the bat that's the middle number and quite frankly you'll hear this word median much more than average okay at least a description of home .

Prices but let's talk about average home price let's say i said oh the average home price is um 350 000. okay so how can we interpret that all right well the average home price is 350 000 let's go back to our city here all right and let's erase the median for .

A second so we'll confuse ourselves and here we are in lovely city y so the average home price is 350 000. well what does that tell me what does it tell me that every one of these little houses over here are 350 000 okay well if the average is three dude people might get that uh you know feeling like okay yeah there's all .

Every all these houses if i go to citywide the average home price is 350 000 uh then you know um you know maybe i can expect to pay around 350 000. well not really because uh the average is kind of deceiving right in a lot of ways we need other statistical measures so you might have like a home over here it's a hundred .

Thousand uh another one that's like 110. uh you got one over here it's 75 000. you got one for 90 000 and let's say you got another one for 125 thousand all right everybody say what the average is this but maybe you've got one house over here that's 625 .

000. now i don't know if this is the average i'm just trying to i'm just kind of making a representation here but all these little guys right here they're kind of close by okay they're like oh these are in a similar you know they're pretty close financially i mean their prices are kind of not that far from one another but .

Then you got this house that's super expensive well guess what when you calculate this out the average is going to be way higher than these prices so you might be deceived if you went by the average now if you did the median here okay let's go ahead and do that now real quick so i have 75 uh let's see here what's the next 90 .

And what's next after that looks like 1 100 and then i had 110 and then i have 125 and then i have my 625 let me make sure i got everything one two three four five six one two three four five six perfect all right so let's calculate the median so what is the middle .

I'm not sure right this is the middle no how about that's the middle no there is no middle well we have to do is take the two uh closest numbers that are near the middle because this is an even amount of uh data okay the last problem we did .

Right up here we had odd numbers okay odd number of numbers so we had one two three four five it was very simple to get the the middle but in this case all we have to do is we just average uh the two middle numbers so between 100 and 110 if i add those up okay the middle will be 105 okay 105. so that will be the median now the median is .

Much more descriptive okay of what's going on here means half the homes are going to be less than 105 and half are going to be 105. so what's the point of uh this video well one is to know the difference between the the median and the mean but uh in statistics you you need to know other measurements as well okay we call .

This uh the measures of central tendency so things like obviously the mean okay the median there's another thing called the mode which i talk about in other videos and then there's the range and then there's another thing which would be very helpful called the .

Standard deviation all right now i'm not going to get into that but you want to know all these values to get a really really accurate picture of what's going on but i think the median for the most part you know like with the home sales and prices and whatnot uh that word shows up pretty frequently so now congratulations you are the 10 .

Of uh common people that are walking around and i don't mean that in a a mean way but you know a lot of people they read this they're confused they think they're oh yeah the median home price they're really in their mind's eye thinking average okay but you can say no no no that's not that means it means this and people will be very impressed .

With you i'm sure anyways so uh with that being said if this video was informative in some way if you liked it in some way please consider uh smashing that like button that definitely helps me out and uh if you're new to my youtube channel please consider subscribing i've been on youtube for 10 plus years i have a .

Thousand plus videos on my channel ranging from basic to advanced math so if you like my teaching style now you can definitely learn a lot from me here but my best math help will be within my math help program okay so with that being said i definitely wish you all the best in your mathematics adventures thank you for your time and have a great .

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