What is the MEDIAN of 2, 4, 6, 8 =? No one should get this WRONG!
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- Опубликовано: 13 сен 2024
- How to find the median given a set of data or numbers.
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You did not point out that, as others realized, the median equals the mean in this case. It would have been better if the inital example had differentmean & median.
Yes, but it is not always the case ...
If you take 2 4 6 10 for example, mean will change, but median is still 5
@@tontonbeber4555 That's was his whole point. He was saying he should have shown an example where mean and median are NOT the same.
@@wingracer1614 Yes, you're right. I didn't read correctly the first post, sorry ...
5
I thought the same at first but I got the right answer doing the average which made me not feel like a dummy.
IMO, given the potential for confusion between Median and Mean, this number sequence isn't a great example really as they are the same.
Well, depending on whether you mean arithmetic mean or geometric mean. :)
5 would also be the average thus adding even further to confusion for people who do not know the difference.
@@MAtildaMortuaryserverironically, you are one of those who doesn't know.
The median is the central value. If there is an even number of values, it is the arithmetic mean of the two central values. In this case 5.
It can actually be *any* value between the two central values, because for all such values, half of the data set is greater; the definition of the median.
thanks, that saves 17 minutes of my life :-)
All Real numbers both greater than 4 and less than 6, fit the definition of a median. So, medians are not necessarily unique to a data set.
The mean and median are both 5
Had to wait 11 minutes to get the basic answer, that was way too long.
He’s got to make money somehow… with today’s expenses, the “average” (mean, median or mode) income for a teacher isn’t just enough anymore, so he boosts his cents with some extra dollars from google… I don’t blame him for using those extra cash tricks…
Unless there is an odd number of entries, the median is the middle two numbers averaged. In this case it's 4 and 6: 4+6=10; 10/2=5. 5 is the median. If the list was 3, 5, 7, 9, and 11, the median would be the middle value, 7.
And if there is an odd number of entries it's even easier since then as you example demonstrates it's the number in the middle. Just mentioning for those reading your comment and missed it.
So ... Why someone has to talk 17 minutes about this, when you can show this in one sentence?
So ... Why someone has to talk 17 minutes about this, when you can show this in one sentence?
So ... Why someone has to talk 17 minutes about this, when you can show this in one sentence?
So ... Why someone has to talk 17 minutes about this, when you can show this in one sentence?
The median is generally considered to be more stable than the average, which is very "outlier-sensitive". This means, that as the video describes, the average jumps up or down very quickly, if there is a statistical outlier in the dataset. The median however doesn't change a lot (if at all) due to outliers.
Generally in statistics, you would use methods like the boxplot to remove statistical outliers before you calculate the mean and median to get a more accurate result.
The mode is even more stable, but does not describe the same value. The mode is the most common value in the dataset. So in the list [1, 1, 2, 2, 2, 3, 5, 5, 5, 5, 6], the mode is 5, while the median is 3 and the mean/average is 3.36. It is absolutely possible to have multiple modes in one dataset (e.g. [1, 1, 1, 2, 2, 2, 3, 3, 3] has the three modes 1, 2 and 3).
Excellent explanation. Thank you teacher!!👍🏽😊
You wrote the OPPOSITE, you meant to write that last sentence: "The MEDIAN however doesn't change a lot (if at all) due to outliers. Ex: 1, 3, 5, 7, 100. Median is 5, regardless of that last, much larger number.
@@freeguy77 whoops... sorry, my bad. I corrected it.
word salad
@@ratratrat59 for you maybe...
The median I think is the number in a set where half of the numbers are below and half are above. Usually I think the number is supposed to be included in the set itself but in this case neither 4 nor 6 works. I’ll go with 5 on a guess as the set of numbers appear to be the counting numbers and 5 splits the set. (This one I think is tricky because I’m not 100 percent sure.)
That means that the median would also be the fiftieth percentile then.
A better example would have the median not be the same as the mean. The difference between the mean, median, and mode variants of average. Lead with something more like the house example.
It has been 40 years since I left school, I have trouble now with the difference between Average and median.
When those in power talk about household income, they use average and include the millionaire because that makes it look so much better, were the median shows how those in power are just pandering to the rich.
You may want to consider when giving a problem to not make the "expected" incorrect answer the same as the actual correct answer.
2, 4, 6, 8 isn’t a great example, because the median and mean are the same. 2, 4, 6, 10 is a better simplistic example. The hours example however demonstrates median more effectively.
I got this correct, but for the wrong reason, since I only found the average (mean) which also happened to be the median, in this case. Thanks to this exercise, I learned something.
Much appreciated!
He should have picked a set of numbers where median and mean were diferent.
Same here... I felt so smart! Should have stopped looking after 30 sec and kept the good feeling!
The 1 second guess for this one is.
5
4 deviates from 5 by 1
2 deviates from 5 by 3
6 deviates from 5 by 1
8 deviates from 5 by 3
Balanced deviations means 5 is the median integer for the input string of 2,4,6,8
that sounds way more complicated tha 20/4 ...
you made something simple, complicated. Good lord!
@@Erlisch1337 20/4 is NOT how you find the Median value. That is the Average.
Which is why the presenter went through such Length to explain it.
unfortunately, the choice of numbers in the data set presented, did not emphasize the difference between Median value and Average Value
@@wyldanimal2 oh I know. But in this case its the same
You might have wanted to use a set of numbers for which the median and the mean aren't equal. They are, in the example you used.
Mess with people's minds a little by having an outlier. Try: 2, 4, 6, 28.
I like the wilder one from @aaronbredon2948 who used 10^10 instead of 28!
We saw that with the house prices, 40k, 50k,60k, and finally 900k.
something interesting for you to consider here, we use P50 and P90 while considering weapons accuracy and precision (differences in these two terms makes for its own good topic), with P50 being the median. Yet this creates a problem in that it discounts concern for excessive miss. One highly errant shot potentially creates really bad consequences.
I have just looked at definitions of median and some say it falls within the set and others do not give that requirement.
If the median is to be within the set it would have to be 4, because like the price is right you go to far you go over.
But using the definitions that say that being in the set is not required the median must be calculated by taking the mean of the two middle numbers.
Using the former definition the use of an = sign in the question is inappropriate as no calculation is required, so it becomes apparent that you are working with the latter definition and thence the median calculated from the mean of the two middle numbers is (4+6)/2=5.
As others have said, the median happens to also equal the mean so to know that you got the answer correct by other than coincidence this is a problem where showing the working is essential for full marks.
What is mode used for? I could see it being essentially meaningless if you have a list like 1,1,2,3,4,5,6,7,8,9,10...
---> The mean and average are not necessarily the same, while they can seem the same there is a difference in their definitions, and there are even different forms of the mean, and that should have been clarified or at least noted so as people encounter it elsewhere they do not become confused or in turn mistrust either you or the other sources they encounter.
That is correct, I even found a great site page that clarifies the difference, but RUclips won't let me post the link, it automatically removes the post.
Thank you so much for sharing all of these videos!! SO HELPFUL!!
not remembering the exact definition, my assumption was both 4 AND 6 were the median, since it's an even number of items in the set.
As a CS degree holder & 20 year software developer, I also have a somewhat negative opinion of people always over-relying on the median. For practical real world data sets, it's actually a pain to calculate since you need to analyze a set to the point that you A) know exactly how many items are in the set B) hold at least half those values in memory so you can pick the middle. Generally this means looping over the data at least 2x... & loops are the most computationally expensive thing you can do. Mean, standard deviation & mode meanwhile can be calculated with a single loop & some relatively efficient variables.
And as for median being 'superior' to mean because it can be misleading... well so can the median. knowing the median of 1,1,1,40,5k,5k,5k is 40 doesn't actually tell you a damn thing about the data set. Providing only 1 value for the average is just either lazy or intentionally misleading, & when giving a combination of values median is generally the LEAST useful for understanding the data.
I'll never forget the time when our local Hotels were running advertising saying how they were good for the economy. They employed about 'x' number of jobs in the city with an 'average' income of $y.
My co-worker and I were full time and I don't think together we earned $y. Most of the hotel's employees were Maids, who were all but a few part time and seasonal. Cooks, janitors also were part time and seasonal.
We both just about fell off our chairs when we realized how much the few at the top must be making. Much like the 'one' house in the neighborhood in the example above.
The median is much more important and relevant than the average/mean. In most cases the mean does not provide much useful information. The explanation is well done (even though the numbers of the initial median could have been chosen differently, to avoid confusion with the mean).
So... I have also seen in many valid mathematical texts the median of an even number of values as being undefined - there literally isn't a 'middle' value.
5 in 3 seconds
However if someone did it incorrectly and calculated the mean, they would still get it right
Yep...I did. I calculated for the average😊
NO, in this case the two statistics are the same, but that is just a coincidence in the data set. MEAN = the average of all the values: SUM of Values / (number of values). Whereas the MEDIAN is the middle number or averaging the two middle numbers.
There is also the Mode. What is the Mode value ?
The word "average" is imprecise. Im statistics it can refer to any measure of the central tendency of a set, whether mean, median, or mode, though it's most commonly used to refer to the arithmetic mean. Generally, this isn't all that important, since for an unsophisticated audience it has only that common definition, but when referring to statistics, it's crucial to be very specific.
5. Median is simply that number where half the values stated are above and half are below. As opposed to the midway point between the stated numbers, and the average which is the sum of all the stated numbers divided by the number of numbers stated. The median in this case is between 4 and 6, and the only whole number that represents that is 5. Of course the average is also 5.
The median and the mean are the same in this problem, so it really doesn't illustrate the important difference between the two concepts.
median is middle half are less half are more . it can be more meaningful that ave . ave can be skewed because of 1 number . like 2,4,6 , 1000 ave = 253 $/hr pay for 4 people.
Why is it important to all. How does it help in our daily lives. How often fo we use median. Average yes
I think it was a poor choice of number because Many people confuse Median with Average
and the Choice of Numbers ended up having the same values for the Median and for the Average.
People who figured out the Average, might see that 5 was correct, and then walked away without watching the entire video.
and the Opportunity to show them their mistake is missed.
The set of numbers 1,4,6,8 or 3,4,6,9 would have been a better choice to emphasize that there is a difference between Median and Average.
If I remember correctly the MEDIAN is not the same as the MEAN (or average).
The MEDIAN is just ''in the middle'' after you have put all the numbers in order, lowest to highest.
2 4 6 8 is already in order .. and 4 and 6 are in the middle .. so the MEDIAN is 5.
However, in this case .. 5 is also the MEAN .. (2 + 4 + 6 + 8) divided by 4
5 is the arithmetic mean. The geometric mean would be 4th root of 384. cheers
Thank you for this simple to understand explanation.
5 is the arithmetic mean. The median of a series of values is the central value when they are arranged in order of size. There is no median here and the concept is irrelevant when a very small group of values is involved . Median is an inappropriate measure of central tendency.
I’ve lived in the real world for almost 50 years and I’ve never needed to use this. Now I know how to figure out the median, and I can assure you that I’ll never use it again. Nothing wrong with knowledge but it’s certainly not something that everyone should know or even anything useful for most people.
What would the 'Mode' of a number series be without repeating numbers or several numbers with the same frequency?
Frankly, in my experience, in places like the news, the usages are something like mean 10,000 : median 100 : mode 1.
It bugs me that the real estate industry constantly used "median house price" when they are actually referring to the mean house price.
This is a great one. I knew what it was as soon as I looked at it but I had no idea why other than median = middle in my head.
Median is good if the variation is high like on income. If the variation is small and even limited like school grades which in Finland are given on scale 4-10 then average is better as every grade counts in it and one has more precision btaddibg a decimal.
Sometimes in median with even number of values one cannot calculate the average of the two like if they are non-numeric. Then one should pick one or present both.
The problem with this example is that both the median and the mean are the same. A better example would have them be different. The house example does this, but in that example the median and the mode are the same.
Here’s a better question maybe: “In this set of numbers what’s the mode?” (I have no idea because each number is unique and the mode, from memory, is “the number in a set which appears the most times.” I don’t know if you can list multiple numbers in a mode but if you can it should be the entire set itself perhaps.)
a distribution can be "bimodal" or "multimodal" and have more than one mode.
Mode = 2; 4; 6; 8
I think a better question is "Who do we appreciate?"
In cases like this we would probably say there is no mode.
The median is the middle point between the highest and the lowest number, whereas the mean is when the sum of all the numbers is divided by the number...of all the numbers. In this case, the mean and the median is 5 and they're equal because there's an even number of numbers that are equally spaced along the number line.
I think i understand what you are trying to say, but the way you wrote it is a little misleading and I've noticed this is the given definition on some dictionaries online :(.
If the median were the middle point between the highest and lowest numbers, then it would always be exactly halfway between the two, but it isn't. It is not the midpoint of the raw values, it is the midpoint of the frequency of those values.
Take the group of numbers of
1, 2, 8, 9, 9, 9, 9, 10
According to what you said, since the lowest number is 1 and the highest number is 10, midway is 5.5
But the median is in reality 9, because we divide the whole set of the data points into 2 equal sizes and find the midpoint between the two.
In the above example,
The first set of data is
1, 2, 8, 9
And the second set is
9, 9, 9, 10
I disagree with this definition, as unlike the average value, the median is much more significant if it is an element of the set of possible values. Hence it is best to have an odd number of elements of the sample set.
Great refresher. Thanks.
Add 4, and 6.. then divide by 2 =5
16:50 to explain this! One look to clearly see the answer. Dear God!
What’s the median grade achieved in a class that gets; A,A,A,B,B,C,C,D,D,D?
B-C
75% or a C
Convert these grdes to their numeric equivalents and go from there.
It should be noted that people confuse median with average.
I learned about all 4 together so even today decades later I think "mean, median, mode and range". I remembered all except for what Mode meant.
(2+4+6+8):4=
20:4=5
Sort the data from least to greatest and pick the middlemost number, which cuts the data into 50% groups. When the number of observations is even, there isn't a unique answer to which is middlemost. One needs to define a way to make a unique answer. The arithmetic average of the two middle-most numbers is a commonly used convention but in my graduate theory of statistics class we used the smaller of the two because the math worked out nicer for our purposes.
I wish things that are conventions were often indicated as such. At least in my experience as a university instructor, telling students that things like this are choices made by people and not laws of mathematics actually helps them understand that math is a thing done by people... maybe even people like them!
Very good point !
@@philipstokinger130 Thanks. I think a lot of instruction ends up being disempowering for the students. It's all over the place, not just in math, but math is particularly bad.
The median is the grassy part in the middle where you don’t drive.
I assumed it was 5, but the definition of the number in the middle could have implied the number had to be there. But if that were the case, you couldn’t get a median for any 3even numbers. I just watched to make sure I was correct. Thanks 🙏🏼
Presumes that you are dealing with integers. For real numbers it is somewhere between 4 and 6.
Between 2 and 8 is 3,4,5,6,7. What is the middle number?
Woo hoo! Junior high math from the 70’s still works as does my brain!
Why would you use as the fist example numbers, where the median and the average is the same? That is very unfortunate!
its the average of the 2 middle elements when you have an even number of items.
With this set of integers, the median is the same as the mean.
Just a fluke. Try 1,1,1,1,9.
IMHO, {2,4,6,8} is a bad choice of numbers here.
The median is the center comma ,
Statistics. The middle value in a distribution, above and below which lie an equal number of values.
The American Heritage® Dictionary of the English Language, Third Edition copyright © 1992 by Houghton Mifflin Company. Electronic version licensed from INSO Corporation. All rights reserved.
i.e., the middle price of the houses on my street. It seems awkward but it is meaningful to that tricky real estate agent....
I wonder how many people came away thinking they found the mean when instead they found the average. I also wonder how many people now think (or still think) the average and mean are always the same number. I'm sure you're a nice guy, John, but you picked a very poor example.
Should have used an ODD number of numbers to find the median. Then it is always the one number in the middle. Ex: 1, 3, 5, 7, 9. Median is 5 again! LOL
Median and average are the same in this case: 5.
I have always understood that median was the middle of a range. You establish the range through whatever logic fits the situation and then calculate the median. For example, you have five sales of some asset. Four sell for below $100 and one sells for $500. The $500 dollar item is outside of the range so it is excluded and the median is determined using only the asset sales within the established range of less the $100. The most important factor in the calculation is the determination of the range and the logic for excluding some results.
I was taught that average is a laymans term and not to use it.
15:15. You're welcome.
This is a great explanation! What software do you use for your virtual chalkboard?
Whats a median?
The median is the sum of all given numbers divided by the amount of those numbers. In this example, we have the numbers 2, 4, 6 & 8. That's four numbers. So the formula is as follows: (2+4+6+8)/4=20/4=5, making the median of 2, 4, 6 & 8 the number 5. It really is that simple.
That's not the median. That's the arithmetic mean (which just happens to equal the median in this case).
The median of 2,4,6,8 is the same as the median of 2,4,6,10¹⁰.
That's a wild thing to think is the truth with 10^10, but it's true! 4 numbers, so the two center numbers are averaged to get 5.
ha ha ha ha
I loved statistics at school and university. My biology degree course had a set unit of maths (Aussie here) in first year which was half a year of calculus and half a year of stats. In the years since then I have used the statistics from time to time at work but never the calculus and would have preferred doing a whole year of statistics instead!
Perhaps you should have had 90% calculus and 10% statistics instead so you learned to recognize and perform applications for both.
I've had both and use both from time to time even in my spare time. They are just two different math tools and can both be very usefull, just like how a carpenter needs both a saw and a hammer to be a succesfull carpenter, a mathematician needs both calculus and statistics to be a succesfull mathematician.
Sure one carpenter might prefer sawing to hammering, while for another it's just the other way around, but both ought to know how to use each tool and ought to know in what situations they need to pick which tool. Hence I'd consider a carpenter who can't think of any use for a hammer just as useless a carpenter as a carpenter who can't think of any use for a saw.
A blacksmith on the other hand would obviously prefer better skills with a hammer over better skills with a saw for blacksmithing.
Similarly in biology especially population ecology statistics is vastly more used than calculus and as such knowledge of statistics is more valued than calculus within that field. However I'd assume you are far more than merely someone at work as a biologist.
That’s interesting as I had a full semester of each in high school in the US, both at college level (we have a testing program for low level college courses like calculus 1 & 2, so high schools can effectively teach these college courses early for those prepared).
I moved into machine learning around 2010, and AI after that, and agree with you that statistics has been more helpful (for me at least), but I’ve found that discrete mathematics (which had Calculus 4 and Differential Equations as prerequisites where I went to school) has been more useful as it directly helps to characters the data set (this is when you’re writing new models, not simply applying an existing tool to a data set). Though even here Stats 1 is probably the most useful of all of these, though nothing is as important as what I call the Fundamental Theorem of Science, which can be stated numerous ways, but as an example, “If your theory doesn’t accurately predict reality it’s wrong” and its corollary, the Fundamental Theorem of Engineering , “but sometimes wrong is good enough, see Newtonian Physics or Special Relativity” (for context: Isaac Newton was wrong, and Einstein developed the theory of Special Relativity as a simplified version of General Relativity that used a lot less math while still capturing the general essence of Relativity - so he released it even though he knew it was wrong simply because it was useful).
@@robertkb64 The type of calculus we were doing was three dimensional with z squared, y cubed, x cubed etc and every single example we did, x ended up to = null (phi) which meant that the equation could not actually be solved and the 3D shape came to a saddle point which was frustrating to say the least. We had done some basic 3D calculus in our last year of high school, Year 12 (this is in Australia in the 80's) as over here, everyone in the State takes the same exam at the same time for each of our final year subjects in high school and you are graded against everyone else in the state.
To get into my course, you had to have a pass in Chemistry, English and two out of Biology, Physics or a branch of Mathematics (Maths was divided up into Pure, Applied and General) and I had all of them in my last year except for Physics. You needed to have a relatively high score as the course only took in 60 applicants each year.
We had done a lot of 3D geometry in the Maths course I did that year, year 12, plus Statistics, some Calculus as well as some other stuff. We were not allowed to use calculators until year 10 at the time, prior to that you had to use a book of tables to find the log, sine, cosine etc so you had to learn it the hard way.. and not just plug the numbers in and get an answer.
I ended up working in regulatory labs where we had to check our results against the standard deviation etc and at those times, my solid grounding in Stats came in handy because I not only understood how my result fell into whatever section, but what it actually meant.
There are 2 middle numbers so I add then divide by 2
Congratulations!!!
WHAT?! I got it wrong! Never heard of "median". - For me it's this progression : 2,4,6,8 ...10 , or, ...... "who do we appreciate" or, ........."bog in don't wait."
I've heard of, the "mean Temperature ". Now that makes sense. So, it's just, finding out ,"the average". So, if you were to say, " the mean, average temperature ", it would be redundant? How come 13 ÷ by 5 = 2.6 ?
Mean, Median and Mode are all averages.
Mean is the sum of values divided by the number of values.
Median is the middle value (or the mean of the 2 middle values).
Mode is the most common value.
If you have a curve (and not specific values), there are more complicated ways of calculating them.
You're just being MEAN!
7:40: There are three means.
The arithmetic mean of 2, 1, 3, 1, 6 is 2,6.
The geometric mean of 2, 1, 3, 1, 6 is 2,0477.
The harmonic mean of 2, 1, 3, 1, 6 is 1,6667.
It is not confused. It's in every typical basic course of statistics. Answer is 5. Interpolation between 4 and 6 which for 50% is of course average.
You can use exactly the same method for every percentile ... like first quartile (25%).
0.25(4-1)+1 = 1.75 So between element 1 and 2 but with 0.75 interpolation. So first quartile here is 3.5
It's not important for ALL. It's not used ALL the time. It's not important for EVERYONE to understand.
I just added the numbers and divided by four = 5
got it - median is middle - 5
4 + 6 = 10 : 2 = 5 🎉
5. 😊
Ten or twelve?
4+6=10; 10/2=5
Got it just looking at it. Terry from Oz
What's the median of median? It's halfway between f and g.
F 1/2. ROTFL!
Not so simple: if you've got a data set and the set is a set of even numbers then can the median be a number that is not in the set. But setting the arcane aside, why take so long over this single page of statistics 101.
What is the purpose of this math problem
To screw peoples' minds to the max!
(x+2x-2)
The mean is 5.
You made two didactical errors at the start of the video. The first one was that you asked for the median of the numbers 2, 4, 6 and 8, which is an unfortunate choice since with these numbers the average is identical to the median. Secondly you rewarded those wh possibly by mere chance got the end answer correctly without any check whether their calculation was correct. In other words, you asked for the median, but you also gave full marks (happy face and stars) to those who calculated the average instead.
5
5?
It should be four since four is halfway between 0 and 8.
0 is not in the list. Median is the MIDDLE number, or averaging the two middle nunbers if an EVEN number of numbers in the set. Median is 5.
Remember that the median on a highway is as close as you can get to the exact center of the highway.
But if you get too close to that median, and a car does the same coming from the opposite direction...
Shall I Google it for you ?
idiocracy