This video should be played in math class. I knew what both of these are from dry boring math class, but putting it in real examples and making it engaging with real concepts, gives it more value to remember to think critically about what numbers are being presented to you.
Right? Now that I've had it explained in an easy to understand way, I'll definitely carefully look at the type & overall data trends before deciding which way to present average.
Actually for your current draw example, we use the average current for a lot of things. Cellphones, for example. The average current draw of your cellphone at idle (screen off, sitting on a desk) we try to target 5mA. But you have to realize when the phone "checks in" to the tower, it's easily spiking 200+mA. This is because the DSP needs to be woken up, the transmitter needs to send a signal and the RF power amp to send the signal consumes a lot of power (and at RF levels, things aren't terribly efficient). So the goal is to spike it for as short a period of time as possible (usually under 100ms), and to maintain the "off" time as much as possible - you have to keep the receiver powered up, but those can consume very little power. The protocols are designed where the cellular receiver is monitoring the tower signal quality to determine if it needs to hop to a new tower or check in more frequently which is why battery life suffers if you're in a weak signal area.
If you have a product with a predictable repeatable current pattern that included the TX spike, then yes, that would be true. My point was that if you measured a bunch of data points to find a base current consumption of your widget, and it happened to include a random infrequenct large current spike, then that could eronerously increase the overwise "base current" specification. Now that I think about it, not the clearest example, oops.
I remember way back in school 50+ years ago math teaches going over this subject, the visual that you used help my understanding a little more. This video trapped an old player. Keep the videos coming and thank you Dave.
Thanks. I have bored my coworkers with my banging on about why median is important, but they don't have a stats background. I am going to link them this.
Only datasets with positive values were discussed. Sometimes you want to used the 'arithmetic mean' to cancel Gaussian noise, and 'skew' the 'average' towards the 'signal' The 'skewing property' of the mean is also very useful to 'signal' for outliers. Sorting large data set can be significantly 'costlier' than computing a 'mean.'
Median can be deceptive too. For example, if you have a neighborhood where 52% of the homes are under $200k, but 48% are over $500k, the median of let's say $198k is meaningless, no pun intended. Damn English is hard because one word can have a dozen definitions - mean, MEAN, and MeAn. I am not a mean man talking about the mean resistor value to mean students, I mean, but I have the means to mean a really mean mean.
Another thing I didn't remember that I probably learned at University 40 years ago (or maybe even before that). Thanks for the repetition, Dave! So, the median of the numbers 1 and 10 is the mean value of the numbers 1 and 10.
Excellent topic for me who worked in test and measurement for a smart phone company that don't make phones anymore. Before any calculations are made upper and lower limits are decided which will tighten as the production from prototype through the ramping up of production.
A nice blend of mean & median is the weighted average, i.e. award effective points to the individual values based on how close they are to the median value, i.e. emphasizing values closer to the median while down-weighting outliers like 500 without actually disregarding them totally. In this case the weighted average per my calcs = 101.02 Extra: Replace a 101 data point with another 500 and you get = 101.25
The last example was strange. For a circuit running from a constant voltage, the energy usage is going to proportional to the mean current, not the median...
I agree with everything, except the circuit current measurement. You can't just ignore those spikes, since they also consume power. If you pretend that they aren't there, the battery life estimation will be off and batteries will last shorter than expected.
It's wild that we're living in a world where someone needs to explain this to people. Thank you for doing so. And I'm happy to say Canada is 10th in both XD
"Mode' is one that needs using more, especially when they government want to try and say people are better off because that average wage is X but that is not the reality for MOST people. It is more important what the most common wage is .
You'd have to bin data fairly widely first to get this. And then you'd have everyone saying WTF is Mode. It's hard enough to get people to understand Median. Never heard any goverment state the Mode.
Hey, Dave! I did a whole PhD in the 90's on simple analog circuits that calculate the median without explicitly sorting. It's actually pretty easy to do. Also, the median pops up in other circuits in interesting ways. For example, a severely slew rate limited system tends to the median of the input! Same happens for a delta modulator. There's also a class of M-type (median-type) filters which are kind of a controllable hybrid between mean and median with some characteristics of each. I stumbled on this when I was working on circuits to pull out the max and min of many inputs and realized that one circuit could do either with a programming current, and in fact, could get any order statistic - e,g, 2nd lowest, 4th highest. I'll let you twist your noggin on how you do that with a handful of transistors. (You can even do it with diodes!) So what started out as a math lecture can turn into a circuit lecture!
The most important concept about the median is that half the data is below and half the data is higher. That cannot said about the average even as that is the most intuitive impression it conveys.
There's an old book called "How to lie with statistics" that goes over all this. It came out in 1954 ! You think people would've learned by now. My favorite, also in the book, is messing with the scale on graphs in order to manipulate perception. You see that one everywhere.
You might want to know mean power consumption, instead of median because even if spikes in power are infrequent, they still take energy from the battery. Say a sensor wakes up to measure and transmit, then sleeps 10s. The power used will be almost all during the 10ms transmitting, not during 10s of sleep. The median power would be the sleep power!
Well it's the not the first video I comment in the same way where someone explains it. It's very unfortunate that because of this exact example people tend to think that median is "better" than mean. Sometimes they correlate median with better representation of the data and get manipulated. The problem is that median can be used to manipulate in the same way the mean can, just in a different case. Its very nicely seen on open-question exams with a certain level to pass, where graders usually "lift" a bit results just below the limit. In this case the shift in grade cause an x-axis shift and the median becomes to low to be a good representation of the dataset.
Just “restored” (rubbed a bit on the battery terminals and shoved some aluminum foil on the springs) my FILs HP-41C right before Christmas, nice to see yours make an appearance 👍
We use what is called % trimmed mean for looking at data sets at work where we trim the top and bottom 5% numbers of the data set. As far as the global wealth thing goes, I would suspect that it largely has to do with that in the USA you generally don't buy your apartment, you just rent it forever but never build any asset value where in many if not most other countries you buy your apartment and build that asset value. Given that approximately 60% of the US now rents instead of owning a home this has only driven the wealth down as the previous generation it was approximately 60% who owned homes.
Honestly there should be a law or something that requires to print standard deviation (aka how on average is the data off the mean), in any statistics related document.
The mean value is used with voltage standards by using three standards, (three ten volt standards), and calculating the value from the three. I have an old Fluke standard set up this way, having three outputs. Of course, the difference between each might only be one to two parts per million at the most.
Sorry Dave, I disagree with you on using median on current measurements. Mean is more accurate for getting a battery life. Imagine you make your high power peaks twice as often, and those peaks are the majority of the Ah spent, your battery should discharge twice as fast. Your media will hardly change in that scenario. Sure, median might be useful to get the idle power usage for a device, but not for cumulative total power consumption.
I think this would be better to elaborate how median can be very misleading as well. Median tells you nothing about the actual distribution. It's entirely possible that shortly past the median your data falls off dramatically from the median value. This is the case with income especially.
I don't think I have ever used median... only for plotting. If there isn't room for histogram, there is boxplots or if you are feeling adventurous: try a violin plot.
Two things: why is Liechtenstein not in the wealth table? And secondly, if you didn't have a Hewlett Packard 41CX in your calculator collection, wouldn't that drop the average GDP of Australian households?
I just read a statement that uses median in a very specific way; pays its CEO 532x more than it's 'median' workers pay, the company would tell you what the 'mean' pay is.
Since John Tukey, real Stasticians just look at a plot of the distribution, note outliers and look at the quartiles or smaller. I guess Engineers are not visual thinkers.
At 10:20, would it be valid to take the difference between the mean and median for the same country, and rank them on wealth (in)equality on the basis of that number? I suppose it would need to be a ratio rather than an absolute?
Are there ever applications for blending mean and median by taking the mean of a larger number of "middle" values? Eg, the mean of the middle 9 of 1000 values?
Should have also covered the modal averages, especially when discussing things like average wages as because it applies to the most nimber of people it's the most accurate. This is also why things like GDP per capita are useless. Modal GDP would really be an eye opener.
Simple concept, but the explanation is impactful. Also could sniff the sneakiness of using similar sounding words that are drastically different in actual meaning🤔. Etymology of the two words should give some clues as well. Wondering what would be the numbers for BEV battery life might be?(esp. to hide the bad batteries)❤👍
Median doesn't seem to make sense for a large range of values, it is not for "comparing apples to oranges". Yet it is many people's default goto, presumed to be better on merit of somehow being more scientific. Computationally, it is much easier to sum and average than to sort to find the mid point. Averaging can easily be applied with limits to exclude or weight down outliers / identify errors and whatnot.
@@EEVblog Going median itself is literally just throwing out all data except the median value. I'd say a more apt approach would be to categorize, group and handle each sample group individually.
Was hoping for an above average video but it turned out pretty mean
I found it deviated a bit but was ultimately significant...
what a mean comment 😞
I'm tempted to say "Damn, bro, you got the whole squad laughing," but I don't want to be mean.
... but it's integral to understanding the subject at hand.
Well i thing the som of it was fine
Next video: variance and the most important difference between precision and accuracy.
Dave seemed to get a lot of calculators as Christmas presents this year!
I thought I was the only one that noticed!!! 🧮🧮
Politicians get meat, and people get potatoes.
On average, we all got shepherd's pie.
This video should be played in math class. I knew what both of these are from dry boring math class, but putting it in real examples and making it engaging with real concepts, gives it more value to remember to think critically about what numbers are being presented to you.
Right? Now that I've had it explained in an easy to understand way, I'll definitely carefully look at the type & overall data trends before deciding which way to present average.
Actually for your current draw example, we use the average current for a lot of things. Cellphones, for example. The average current draw of your cellphone at idle (screen off, sitting on a desk) we try to target 5mA. But you have to realize when the phone "checks in" to the tower, it's easily spiking 200+mA. This is because the DSP needs to be woken up, the transmitter needs to send a signal and the RF power amp to send the signal consumes a lot of power (and at RF levels, things aren't terribly efficient). So the goal is to spike it for as short a period of time as possible (usually under 100ms), and to maintain the "off" time as much as possible - you have to keep the receiver powered up, but those can consume very little power. The protocols are designed where the cellular receiver is monitoring the tower signal quality to determine if it needs to hop to a new tower or check in more frequently which is why battery life suffers if you're in a weak signal area.
If you have a product with a predictable repeatable current pattern that included the TX spike, then yes, that would be true.
My point was that if you measured a bunch of data points to find a base current consumption of your widget, and it happened to include a random infrequenct large current spike, then that could eronerously increase the overwise "base current" specification.
Now that I think about it, not the clearest example, oops.
Actually is the receiver that draws more power (because of the active filtering and signal processing) and should be powered just at the precise time.
A: You are mean?
B: You mean I'm average?
A: I mean mean
B: Average average?
Who's on first?
I remember way back in school 50+ years ago math teaches going over this subject, the visual that you used help my understanding a little more. This video trapped an old player. Keep the videos coming and thank you Dave.
He's a good teacher
Mean are the house prices. Absolutely bonkers.
Thanks. I have bored my coworkers with my banging on about why median is important, but they don't have a stats background. I am going to link them this.
Only datasets with positive values were discussed. Sometimes you want to used the 'arithmetic mean' to cancel Gaussian noise, and 'skew' the 'average' towards the 'signal' The 'skewing property' of the mean is also very useful to 'signal' for outliers. Sorting large data set can be significantly 'costlier' than computing a 'mean.'
Median can be deceptive too. For example, if you have a neighborhood where 52% of the homes are under $200k, but 48% are over $500k, the median of let's say $198k is meaningless, no pun intended. Damn English is hard because one word can have a dozen definitions - mean, MEAN, and MeAn. I am not a mean man talking about the mean resistor value to mean students, I mean, but I have the means to mean a really mean mean.
True, that's why I like looking at the shape of histograms for a better picture
Another thing I didn't remember that I probably learned at University 40 years ago (or maybe even before that). Thanks for the repetition, Dave!
So, the median of the numbers 1 and 10 is the mean value of the numbers 1 and 10.
Excellent topic for me who worked in test and measurement for a smart phone company that don't make phones anymore. Before any calculations are made upper and lower limits are decided which will tighten as the production from prototype through the ramping up of production.
A nice blend of mean & median is the weighted average, i.e. award effective points to the individual values based on how close they are to the median value, i.e. emphasizing values closer to the median while down-weighting outliers like 500 without actually disregarding them totally.
In this case the weighted average per my calcs = 101.02
Extra: Replace a 101 data point with another 500 and you get = 101.25
Yah, you can clip your averages but then you need to justify why. That can be controversial.
Thank you leaving that clip in!!! I laugh every time I see it!
"That's the news from Lake Wobegon, where all the women are strong, all the men are good-looking, and all the children are above average."
Thank You Dave!
Dave, you are such a good teacher!
Very subtle with the calculators :)
Have a happy holidays EEVblog
Can you do a follow up on standard deviation ?
The last example was strange. For a circuit running from a constant voltage, the energy usage is going to proportional to the mean current, not the median...
Yes and it should be time-weighted
Almost 1M! Been watching you for a while!
I agree with everything, except the circuit current measurement. You can't just ignore those spikes, since they also consume power. If you pretend that they aren't there, the battery life estimation will be off and batteries will last shorter than expected.
I was explaining this to my friend, only yesterday. I will send her your video to watch.
It's wild that we're living in a world where someone needs to explain this to people. Thank you for doing so. And I'm happy to say Canada is 10th in both XD
"Mode' is one that needs using more, especially when they government want to try and say people are better off because that average wage is X but that is not the reality for MOST people. It is more important what the most common wage is .
You'd have to bin data fairly widely first to get this. And then you'd have everyone saying WTF is Mode. It's hard enough to get people to understand Median. Never heard any goverment state the Mode.
@@EEVblogThe "mode" is derived from "moda" in italian that means (npi) "fashion"... most used value
The mode would probably be close to zero in a lot of these real world cases (wealth,income etc) ;)
3M must have used mean to come up with the max load Command strips can carry.
@@EEVblog Basic Stats should be a highschool course.
Reminds me of the book we used in highschool maths - "Mean, Mode, and Median, the truth about averages"
Very interesting and helpful.... Thanks Dave
Hey, Dave! I did a whole PhD in the 90's on simple analog circuits that calculate the median without explicitly sorting. It's actually pretty easy to do. Also, the median pops up in other circuits in interesting ways. For example, a severely slew rate limited system tends to the median of the input! Same happens for a delta modulator. There's also a class of M-type (median-type) filters which are kind of a controllable hybrid between mean and median with some characteristics of each. I stumbled on this when I was working on circuits to pull out the max and min of many inputs and realized that one circuit could do either with a programming current, and in fact, could get any order statistic - e,g, 2nd lowest, 4th highest. I'll let you twist your noggin on how you do that with a handful of transistors. (You can even do it with diodes!) So what started out as a math lecture can turn into a circuit lecture!
Regarding the median the percentiles, being the more general concept, would also have fitted in here. "75% of all values is bigger than X"
101 is also the "mode" in your example where the median is 101. :)
Thanks for mediating these mean tactics for the average person.
Love this calculator showcasing video! I have an HP like at 0:50, played with programming it when I was a student :)
The most important concept about the median is that half the data is below and half the data is higher. That cannot said about the average even as that is the most intuitive impression it conveys.
There's an old book called "How to lie with statistics" that goes over all this. It came out in 1954 ! You think people would've learned by now. My favorite, also in the book, is messing with the scale on graphs in order to manipulate perception. You see that one everywhere.
Fantastic, Thank you Dave. I think you had room to talk about RMS at the end too, ( with this being an electronic channel )
I've missed the whiteboard classes. Cheers! 🎉
You might want to know mean power consumption, instead of median because even if spikes in power are infrequent, they still take energy from the battery.
Say a sensor wakes up to measure and transmit, then sleeps 10s. The power used will be almost all during the 10ms transmitting, not during 10s of sleep. The median power would be the sleep power!
Yeah, admitted not the best explained example. See my other reply.
Mode is also imprtant. You can have two data sets where the average of one set has increased, the median stays the same and the mode decreases.
Well it's the not the first video I comment in the same way where someone explains it. It's very unfortunate that because of this exact example people tend to think that median is "better" than mean. Sometimes they correlate median with better representation of the data and get manipulated. The problem is that median can be used to manipulate in the same way the mean can, just in a different case. Its very nicely seen on open-question exams with a certain level to pass, where graders usually "lift" a bit results just below the limit. In this case the shift in grade cause an x-axis shift and the median becomes to low to be a good representation of the dataset.
Just “restored” (rubbed a bit on the battery terminals and shoved some aluminum foil on the springs) my FILs HP-41C right before Christmas, nice to see yours make an appearance 👍
We use what is called % trimmed mean for looking at data sets at work where we trim the top and bottom 5% numbers of the data set.
As far as the global wealth thing goes, I would suspect that it largely has to do with that in the USA you generally don't buy your apartment, you just rent it forever but never build any asset value where in many if not most other countries you buy your apartment and build that asset value. Given that approximately 60% of the US now rents instead of owning a home this has only driven the wealth down as the previous generation it was approximately 60% who owned homes.
Well explained.
Geometric mean is also very useful at times. For example the midrange of audio: sqrt(20x20000)=~ 632 Hz
Awesome, I'm glad to see that I'm not the only one who collects portable calculators used in daily life to this day, awesome.
My mother inlaw is mean. And she’s definitely not adv.
Honestly there should be a law or something that requires to print standard deviation (aka how on average is the data off the mean), in any statistics related document.
The mean value is used with voltage standards by using three standards, (three ten volt standards), and calculating the value from the three. I have an old Fluke standard set up this way, having three outputs. Of course, the difference between each might only be one to two parts per million at the most.
Its interesting to note that RMS favors the large outliers! With your data set the RMS is 178.6 !!!!!
so many calculations, so many calculators
Sorry Dave, I disagree with you on using median on current measurements. Mean is more accurate for getting a battery life.
Imagine you make your high power peaks twice as often, and those peaks are the majority of the Ah spent, your battery should discharge twice as fast. Your media will hardly change in that scenario.
Sure, median might be useful to get the idle power usage for a device, but not for cumulative total power consumption.
Yeah, now that I think about it, not the cleaest example. I was thinking of idle power usage in this instance.
I think this would be better to elaborate how median can be very misleading as well. Median tells you nothing about the actual distribution. It's entirely possible that shortly past the median your data falls off dramatically from the median value. This is the case with income especially.
Love that Swiss Micros DM42!
I don't think I have ever used median... only for plotting. If there isn't room for histogram, there is boxplots or if you are feeling adventurous: try a violin plot.
Two things: why is Liechtenstein not in the wealth table? And secondly, if you didn't have a Hewlett Packard 41CX in your calculator collection, wouldn't that drop the average GDP of Australian households?
I just read a statement that uses median in a very specific way; pays its CEO 532x more than it's 'median' workers pay, the company would tell you what the 'mean' pay is.
Is that why they throw out the high and low in some cases?
Since John Tukey, real Stasticians just look at a plot of the distribution, note outliers and look at the quartiles or smaller. I guess Engineers are not visual thinkers.
Good video as always Dave. Can you explain RMS and regular filtering. Like kalman perhaps
I bet the whiteboards are (barely) velcroed to the wall.
How many calculators do you have? Dave: „Yes.“
More teachy videos Professor Dave!!
Where did that list of averages come from? I *must* find out what _all_ of them are used for!
Would be good to know about what RMS is and why it used in measurements.
Median is the middle of the road. But not the average of the road.
Great video Dave! Saw Norway on 9th place on both, that means we're extra great, right?
...Glad you weren't mean and have included the RTW (Rooting The Whiteboard).
Smarter than the average podcaster...
Great video, good explanation. Now do an ESDM.
In statistics there is also 'mode', or the most common value in a set of values. In this case it also happens to be 101 ohms...
Nice calculators collection ;-)
Great explanation, but what about mode?
How many different models did you see... Nice
I only know two things:
1. The price of my rent is mean.
2. I only know one thing.
The really bad thing about the housing example is, ask them to show you the data. And they will either: cry, run or look at you're stupid.
Obligatory YT engagement comment Dave :-) loved the video!
At 10:20, would it be valid to take the difference between the mean and median for the same country, and rank them on wealth (in)equality on the basis of that number? I suppose it would need to be a ratio rather than an absolute?
Meaning to use median as mean means they are being mean.
Also in this case a trimmed mean might be useful.
Perfect
does this include the whiteboard falling or did it get edited out ;p
also nice calculators 👍
Did you measure these resistors?
Are there ever applications for blending mean and median by taking the mean of a larger number of "middle" values? Eg, the mean of the middle 9 of 1000 values?
Can you do a video on RMS
Should have also covered the modal averages, especially when discussing things like average wages as because it applies to the most nimber of people it's the most accurate. This is also why things like GDP per capita are useless. Modal GDP would really be an eye opener.
Video was already longer than I wanted.
People say I am mean when I correct them on the incorrect use of median.
Awesome
Simple concept, but the explanation is impactful. Also could sniff the sneakiness of using similar sounding words that are drastically different in actual meaning🤔. Etymology of the two words should give some clues as well. Wondering what would be the numbers for BEV battery life might be?(esp. to hide the bad batteries)❤👍
I'm surprised Slovenia apparently has a higher median wealth than Germany and Austria.
Dave saving the world from statistical manipulation.
"No calculators/whiteboards were harmed in the making of this film." 🙃
I wish you were my school teacher!
What would be the median of all of those calculators? 😅
Now the only mean question is on avarice how many calculators is Dave showing en median time!
Mean, Median, Mode
Casio fx82 @7:28 🥰
Median doesn't seem to make sense for a large range of values, it is not for "comparing apples to oranges". Yet it is many people's default goto, presumed to be better on merit of somehow being more scientific. Computationally, it is much easier to sum and average than to sort to find the mid point. Averaging can easily be applied with limits to exclude or weight down outliers / identify errors and whatnot.
It makes sense when you can't just throw out data, like in the wages, wealth, and house price examples I gave.
@@EEVblog Going median itself is literally just throwing out all data except the median value. I'd say a more apt approach would be to categorize, group and handle each sample group individually.