The other massive misuse of average I keep hearing is people referring to the life expectancy at the XVIII century. Yeah it was 40 something but not because it was very rare for people to reach 60, but because the average is dragged down by the high infant mortality rate. Once you reached 20, your life expectancy was a bit lower than today, but it was common for people to reach 60.
And in general people are really bad at thinking in term of distributions. If you discuss averages or percentiles, people identify to that metric like if it applied to every individual of that distribution. That makes the debate on D&I particularly unproductive.
People don't generally understand premodern demography. We have fairly good demographic record of England, where detailed birth and death records were kept.
As of the 18th century, about 30 per cent of people died before reaching adulthood, but this percentage seems to be much higher in urban areas, which acted like population sinks. (Pathogens were really concentrated there.) Once you lived to be 20, you had more than even chance to live to 40, and a good (AFAIK over 35 per cent) chance to live to 60, but the drop-off after that was steep, 70 y.o.s were already uncommon and 80 y.o.s very rare.
Interestingly, cardinals and popes lived significantly longer, 70-somethings were a common sight in conclaves. Easier life, no military threat, good water, almost no risk of famines.
I am writing this from the top of my head, so precise values may differ from my handwaving. But I believe that the values are roughly correct.
Hmm based on your comment, I think people understand better than you think. Obviously if the life expectancy is 40, then some people live longer. Half of all people who live to 20 dying before 40 is probably what most people think of when they think about a 40 year life expectancy.
I don’t know specifically about that time period, but there have been dips and peaks in life expectancy over time. In the latter half of the 19th century in England, life expectancy at adulthood was the same or better than it is today.
There was actually a major, severe DECLINE after that associated with globalization, trade, and further industrialization, which is where many charts begin.
Think about how incredible that is - nothing we would recognize as modern medicine, but adults living just as long. I can’t think of any greater indictment of our health in modern civilization, especially given the amount of resources we expend. I mean, just think about - aside from the improvements in child mortality which are almost entirely just from now nearly century old antibiotics and vaccines technology, we spend 20% of our GDP to achieve the same results as the 1850s English who got them for next to nothing in comparison. Progress!
If you want to look at the silver lining, we have much easier lives and access to a tremendous number of cheap, rich foods (albeit unhealthy) and plenty of cheap recreation and drugs. We have worse living habits than them and spend much more time in sedentary positions. It’s probably impressive we can keep the same life expectancy with all those factors.
> we spend 20% of our GDP to achieve the same results as the 1850s English who got them for next to nothing in comparison.
I have to assume that our lives are overall much easier medically, though. Breaking a limb (or even losing one) is not nearly as big of a deal now than it probably was then, for instance.
IIRC bulk of the gain in average life expectancy over the last 2 centuries came from reducing infant mortality, which had outside impact on the aggregate mean.
Our World In Data has a plot of conditional life expectancy throughout recent history. It's one of my favourite plots of all time not because it's important, but informative and intuitive.
Another very powerful demographic chart that I lost (in case someone knows where it is) is a 3 dimensional chart. Y axis is children per women, X axis is infant mortality, and then there is a slider to look at the evolution through time. All countries are plotted as points.
The reason it is powerful is because by moving the slider you can see the evolution through time. For most now developed countries, infant mortality and children per women both reduced simultaneously as the progress of medicine and the evolution of society have been very gradual. But african countries are following a different path, where the infant mortality collapsed but is not followed by a reduction of children per woman (only a few countries have started to take that turn). That is basically all you need to know to explain the major demographic shift we are about to observe in Africa.
It's exactly that, thank you. The version I saw didn't change the scale when you move the slider which makes it easier to see what is going on, but I am pretty sure it must be earlier version of that chart.
And the sharp increase around the mid 1940s is quite remarkable too. I was wondering what caused that, I guess the polio vaccination started getting rolled out but I don't if it was that big of a cause of death.
People don't generally understand how statistical metrics are supposed to work. The whole point of statistics is to give you reasonable expectations for the possibilities of a space that is both full of variation but well-explored based on what particulars you know already. The problem is that most people don't realize the arithmetic mean is intended to give you the expectations associated with not knowing essentially anything. It's the map you give a stranger in a strange land (am I using that reference right? I haven't actually read the book yet); the way I explain how to get somewhere in my hometown to a family member isn't just not the same as the way I would to somewhere near my new job, but runs a worryingly high chance of making things less clear than if they just tried to do it themselves (well, at least, before the days of google maps. Why does technology have to be so good at ruining metaphors?). When you have, or will have, information, working without it is just asking to get tripped up. This the brilliance of the adjustable cockpits example: The Air Force leadership assumed they couldn't set cockpits to fit their pilots because they didn't currently know which pilot would fly which plane, forgetting that no plane takes off in the Air Force without the leadership telling a particular pilot to get in a particular plane. Once they adopted the life-like "What do I know about Y given what I (will) know about X" approach over the card-table-like "What do I know about Y given I can't know anything about X", seemingly untouchable problems immediately resolved out almost on their own.
Blood pressure medicine is probably one of the biggest factors in pushing adult life expectancy past 60. Antibiotics get all the credit but I think their biggest demographic impact was reducing child mortality from middle ear infections.
> Once you reached 20, your life expectancy was a bit lower than today, but it was common for people to reach 60.
If you were a man. If you were a woman, there was still the high risk of maternal mortality. Add to that the large number of births, and a significant amount of women died during pregnancy/birth/post-birth.
> If you discuss averages or percentiles, people identify to that metric like if it applied to every individual of that distribution. That makes the debate on D&I particularly unproductive.
Damore included a graph of overlapping bell curves in his document to illustrate this point. Yet quite a lot of critiques I saw don't seem to understand that.
The thing that stands out is the difference between the bell curves - the area under the male height curve that is not under the female one. (Indeed, on this page, the way they drew their histogram version of the curve they explicitly drew attention to this area)
But this area isn’t representative of a meaningful population.
It’s just the sum of the excess number of men of a given height over and above the number of women of the same height.
Crucially, the vast majority of men accounted for within that population are still shorter than some women.
Unless you are, according to these numbers, over 77” tall - ie, over 6’5” - then there exist women who are taller than you.
Admittedly the population of people taller than you certainly skews heavily male - but for any randomly selected group of men, in most cases it is possible to find a group of just as many women who are all taller.
I personally find that the overlapping bell curve illustration obscures that understanding, making it emphasize more that a small number of below-average men are still taller than some women, and completely hiding the tail of outlier men on the left who are shorter than the vast majority of women…
Stacked histograms are a better way to visualize this kind of faceted distribution - but even that has issues.
> the area under the male height curve that is not under the female one.
It's not obvious to me. Yes the height of the male graph is lower, but is spread wider.
> It’s just the sum of the excess number of men of a given height over and above the number of women of the same height.
It's simply that the female histogram covers part of the male histogram.
It's a bit confusing. If I make the graph I will colour the overlapped parts a different colour.
This is not a problem when we show only the bell curves.
Issue I have with averages is they never say how worked out as often they will use a method that suits the outcome they wish. You get different results from mode, medium and mean averages and can cherry pick wich one fits the narrative and use that with the label `average` and it's just accepted by the majority.
Personaly ALL averages should list all three averages for context and clarity as they do offer a greater insight.
Yes, it can be a problem and I agree more context like median or a full histogram should be more common, but I have never seen anyone claim that the average was 2 in your example.
While the average value was 3.4, I don't think it would be unfair to suggest the average person would have scored a 2 (or whatever the relevant scenario is).
I was always bemused that the average family size was 2.4 children as no family fits that average ever. With mode and medium that would not happen.
Of note I have no idea what the average family size is children wise, just going on longstanding data from UK that in itself may be out of date, though does highlight the point.
Yet if we set up a game with a penalty proportional to the distance between your guess and the true number of children for a family, and you guess the median or mode, you'll be right more often than I (because I will never be right), but you will also continually be losing money to my guess of the mean.
What matters in real life is generally not how often you are correct, but rather by how much you are wrong. What you need to minimise is not your error rate, but the consequences when you are wrong. You are free to make an infinite amount of mistakes, as long as you are sure to make them in such a way that they are comparatively insignificant.
> Yet if we set up a game with a penalty proportional to the distance between your guess and the true number of children for a family, and you guess the median or mode, you'll be right more often than I (because I will never be right), but you will also continually be losing money to my guess of the mean.
Not sure were you went there, but the point is that you can overdetail in a way that abstracts from reality.
It depends on your definition of "very common" of course, but I have come across people using "average" to mean both "typical" and "most common" and "middle of the range" and "my preference" and a whole slew of other things.
Mean, mode, median; they're all summaries. People even in science-adjacent fields are still often used to communicating a summary without showing the dsitribution. If possible, I always ask for both mean and median; it's an indication how off-normal the distribution is.
The mean only has meaning for normal distribution, so it's my least favorite summary, because it assumes the most. Imho the normal dist is assumed way too often.
But isn't the average the useful metric for this question. The question being "If I was born in the 18th century how long would I live". Dying as a baby is a valid outcome.
Maybe the question should be "If I lived past 1 years old what is my average life expectancy?"
It is helpful to say that at first quintile they died at around 10 years of age and at last quintile they died at around 70 (with a median at 33). The average may remain 40, but you get a better idea of the distribution.
The data point you want to use is the modal age of adult death, but everyone is fixed on the mean age of death, which you correctly note is completely skewed by childhood mortality.
Another way of looking at it is that's even worse though. Today, it's very rare to have to deal with the death of a child; then, almost everyone had to go through that. And to say, "once you reached" should really be "if you reached".
My wife worked on the project to upgrade the C-5 cargo plane's cockpit. She's 5 feet 1 inch tall, so she was chosen as the test person for the 5% end of the usability range. If she couldn't reach or operate a control in the cockpit it was a problem and the control had to be redesigned.
My wife is 4'10" and often has trouble finding cars in which the driver's seat can be adjusted to fit her... I'm guessing she's well below the 5th percentile (at least in the US).
Why does this article not even once mention that average could mean "mean", "median" and/or "mode"? Even the title alludes to one of the biggest problems in the domain and that is that many people don't even realise that there is more than one way to measure an average.
There are plenty of examples of where the mean is not representative of the sample and where mode or median would be more realistic, particularly where some large outliers in a relatively small sample would skew the mean.
Likely the same reason that when someone says "mean", they never bother to specify whether they're referring to the arithmetic mean, the geometric mean, or the harmonic mean. :P
Because for the purposes of the article, it just doesn’t matter. The point is to stop distilling data down to a single point, regardless of what math term you want to use.
I think because the moral of the story is the same, which is the airforce switched to customizable controls to support the range instead of over focusing on a single “average”.
Probability and statistics should have already replaced algebra and calculus in modern education. People are just really bad at understanding variance and the impacts on what we think we know.
Anecdata (I wanted to be a teacher earlier on until I actually met a few and heard their stories):
Teachers are generally pretty progressive (both in the political and innovation senses), but the legislation (like Common Core), state & district educational standards, and school boards move more slowly. And in the US, the primary schools are largely funded and overseen by local parents (municipal and state), so the school priorities and cultures partially reflect local priorities.
There's often debate between what individual teachers want to teach (a product of their individual preferences and backgrounds and values) vs what the administration forces them to teach (as a reflection of the political and business realities of their particular school). There's often a personality difference between the two classes too (educators vs admin types), with the former often being (at a stereotype) starry-eyed idealists and the latter being grounded management types with an eye on the numbers of finance and politics; on top of that, there is also often a labor vs mgmt (not quite "owners") divide, with individual teachers being pretty much powerless to teachers' unions being really strong in some districts. Long story short, teachers can't unilaterally change the curricula they teach.
The power struggles affect everything from math (new math, math wars, whether to test it, etc.) to social studies (CRT, Native studies, bilingualism, religious studies) to science (evolution, climate) to business needs (cursive vs typing, algorithms or letterheads), etc.
Far from being a settled matter, our educational system is heavily political and its lack of progress is probably reflective of our divisiveness as a country, where two broad sides keep playing tug-of-war and veering towards the extremes, making tiny gains and losses back and forth.
Without the simple algebra taught in high school neither probability nor most interesting (high school) math would be possible. But a stronger emphasis on probability and statistics would indeed be interesting.
You need algebra and calculations calculus to do anything theoretical in probability. But I'm a fan of working backwards from interesting applications of algebra to the fundamentals.
True, but hardly anyone does anything theoretical. Those who do will probably have taken a lot of extra math courses along the way. IMNSHO, you need to understand the principles of algebra and calculus, but you don't have to know how to integrate by parts, or know the formula for computing the roots of a quadratic. Statistics, otoh, is fundamental to understanding science, voting (I'm thinking of Trump's claim that it was statistically impossible for him to have lost), health, the meaning of bad test results (here I'm thinking of Bayes' Theorem--and minimal algebra is needed to solve that equation), and so forth.
Wow, I've been saying that for a long time. I took algebra, calculus, and probability and statistics back in high school/ college. Guess which one I've used since then, and which two I have not used (with the exception of helping my children with their algebra homework).
The other common misuse of averages I keep hearing confusing "the average X" with "the X of the average Y". (Known formally as Jensen's inequality.)
So for example, the average time to review a code change is not the same as the time it takes to review a code change of average size.
The average user experience of a website is not given by the user experience of the average response time.
And so on. People tend to compute the average of an easier variable and then forget that the derived value of interest is often nonlinear in the easier variable.
There was this Roman poet, Trilussa, which created a good description of why averages are bad, which is known in Italy as "Trilussa's Chicken"
Roughly translated, it goes as follows:
"Following the current statistics, it turns out you're expected to be able to eat one chicken per year, and, if you can't afford it, it goes into the average anyway, because there's someone else out there eating two".
Rome had a conception of statistics? That's very interesting. I'd always been told that it was a relatively new science coming from french aristocracy gambling or something.
Sorry, it's modern Roman, not ancient. Trilussa wrote in Romanesco, which is a Central Italian dialect (Tuscan and central Italian form a somewhat of a linguistical continuum, while southern Italian and northern languages are not mutually intelligible).
I too read "Roman" to refer to empire. Maybe because of the Latin-sounding single name, or maybe because I'm used to identifying people by their nationality rather than their city.
Thank you for sharing. This is the first chapter from Todd Rose's excellent book The End of Average. In the book, he also touches on the fascinating topic of context. For example there is no such thing as a person's average level of aggression - IF I am around my parents I tend to get aggressive, but IF I am around friends and strangers I am calm.
Even Rose's article (I haven't read his book yet so I can't really say about that) tiptoes around what was going on here. It wasn't just a naive application of statistics. Rose gets through the Norma story without mentioning eugenics once, but the whole episode is so obviously part of America's pre-WWII eugenics swoon. Beyond specific beliefs about politics, race or genetics, but linked to them, there was a whole Zeitgeist, the collectivist spirit of the age that gave us Busby Berkeley musical numbers https://www.youtube.com/watch?v=ysvQ5MaUbd8 and the IBM company songbook https://www.networkworld.com/article/2333702/a-history-of-si... . This was a time when it was acceptable, indeed it was progressive, to be violently hostile to difference or defectiveness: see for example War Against the Weakhttps://waragainsttheweak.com/ and, maybe most especially, The Black Storkhttps://global.oup.com/academic/product/the-black-stork-9780... . And of course it's no coincidence that the pioneers of statistics tended to be particular fans of eugenics themselves.
Unfairly or not, the OP does feel like a summary of Todd Rose's own "When U.S. air force discovered the flaw of averages", an excerpt from The End of Average, which you linked there. Rose's article has been strongly upvoted here several times over the years.
And yet, 70 years afterwards, all we have is average ratings of everything, from tv shows to restaurants. Not to mention inflation, any kind of prices dynamics and wages.
Yup, and the most common usage is product ratings on Amazon, which I find a complete waste of time, even before they became corrupted by massive rating-spamming. The metric I find useful is the ratio of negative (1-2 star) reviews to positive, in the product category (some categories seem to have higher usage failure rates, or POd users or something).
It's still possible to get somewhat of an accurate understanding of what you're buying if you read some reviews.
I read ~10 two star reviews, ~10 four star reviews, much more depending on price. One stars tend to be full of stuff like "product hasn't arrived", "garboage", user errors. Five stars are plagued by spam and paid reviews, and also a lack of details. Three stars seem to be split between very picky buyers (esp. hate the "I paid $3.50 for this and it's not the omega particle!") and people afraid to leave lower ratings for reasons.
Agree for sure, and some good notes there! (My comment was merely limited to scope of the averages issue.)
Definitely must read a decent sampling to see if there's a common problem, or it's mostly just malcontents, delivery issues, or misunderstanding the product or instructions, or just random issues. I've found in doing this that I'm usually surprised on the good side.
"If bill gates gets on a bus, on an average everyone in the bus is a billionaire". Read this somewhere and this made me understand why just the average on its own does not say anything.
I would agree that on average each bus rider has a billion dollars, but I can't find away to justify that each person is a billionaire on average. Maybe it is because money is continuous whereas billionaire status is binary, so averaging it out doesn't really make sense.
Then the opposite would be true (and equally nonsensical). If billionaire is a binary status, then Gates, Musk, and Bezos could get on a bus, and on average there are no billionaires on the bus.
Average by itself doesn't tell much.
Average and standard deviation computed over multiple samples from the population tells a lot.
Learning about the various types of standard control charts is quite useful for data-based decision making and monitoring the health of a process.
Control charts and Pareto chart of root causes of defects are two of the basic tools one needs to establish 'basic stability' in a process. Basic stability is a requirement before working on improving a process.
This is a poor analogy - usage statistics tend to not follow Gaussian distributions, hence the average can be a poor measure of central tendency. Body measurements usually don't have that problem, and I suppose that the average was actually used as the 'starting point', from where pilots could customize. For other distributions, one might actually prefer to opt for a different statistic altogether.
There's a better piece on this, which I read several years ago. The core of the problem isn't the use of the mean, which is what most of the comments are picking up on here. The problem is the Air Force was designing for the mean of more than a dozen measurements, which weren't highly correlated. In that case, even if your distributions are Gaussian, you're going to have vanishingly few samples that are on the peak on all of them, which is what the non-adjustable cockpit design optimized for.
If you ever check the average, always make sure to _at least_ add in the median. I don't know if there's any special syntax for this with symbols or whatever but having the median,average,and possibly even n together is way better than just the average.
Probably off-topic, but: Myers Briggs seems to be based on the idea that its four properties are each dichotomous, e.g. most people are either introverted or extroverted. I would imagine that the tendency to be Y-troverted is in fact more unimodal than bimodal--if so, most people would be somewhere in the middle on most traits. Of course if the traits are not independent, that might mean that there are not many people who are in the middle on all four traits; but if they are independent, then I would expect a substantial number of people to be somewhere around average on all four traits. How broad that "somewhere around" number would be, I have no idea.
To think that aircraft safety (military or not) improved because the cabin dimensions were adjusted is laughable. No, it was procedures and systems such as advanced autopilots, better and better ils, gps, gpws, tcas, understanding of crew resource management, textual comms like acars, better maintenance procedures, better operational procedures (even for seemingly simple tasks like deicing) ...
The thing that confuses me is that the second example shows a histogram of the user activity which appears to be not a normal distribution. But for pilot dimensions, I would expect the histogram to actually follow a normal distribution. I feel the problem (and answer) of the cockpit design is presented a bit too simplistic here.
Average is great when you really care about the total, and want the total expressed per thing. For example, if you make 100 investments, the average return is just a way of talking about the total return on all your investments, expressed per investment.
I find that I want the median or the mode far more often than I want the mean. I don't understand why the latter has subsumed the former. I guess it's easier to calculate?
The problem of “average” is that you try to use one statistics to rep a population. Even for bell curves you need 3 - bell curve (normal dist.), mean and std. dev.
This also comes into play with the current discussion of EVs. People will say, "you don't need that 500 miles of range." Or, "just plug the EV in at night - you don't have to wait at the charger."
That probably works well for average use cases, but not for the outliers.
The great thing about ICE vehicles is you generally don't have to worry about non-average use cases. To reach parity, EVs will need to be chargable in 5 minutes from empty to achieve 500 miles of range, at 5 degrees F, with 5 year old batteries. If you live in California, that may seem like an extreme use case, but it's pretty normal around here.
EVs don't need to entirely displace ICEs. Many zealots think so, but it isn't even necessary from an environmental perspective.
But I think the main complication comes to ownership. Are you going to own an EV and an ICE? Or are you doing to own and EV and rent an ICE when needed? Or the other way around? And even if you rent it can become complicated. Last weekend I rented a car and it needed to be an EV since I booked it late and that's all that was late. I personally would rather not have dealt with the extra complexity of charging it compared to just putting gas in the tank.
But really I thin the issue is that if we move to EVs it kind of forces some sort of vehicle specialization where it previously didn't feel as necessary. That opens a big can of worms when it comes to changes in lifestyle for many people.
In general, people often don't optimize for their average use case like commuting or going to the grocery store. They optimize for weekend recreation, buying lumber, the occasional long drive off the beaten path, etc. Some of it isn't entirely rational. But it's also the case that, for many of us, renting a car is a bit of a pain and it's often hard to depend on renting a more specialized vehicle if you need one. So if you're just going to own one vehicle, you tend to buy one for the 10-20% case, not the 80% case.
I'm surprised you can rent an EV. Few hotels have a place to charge them, so there goes the idea of plugging them in overnight, which is the main advantage of EVs
If the EV market could agree on a battery size and configuration, then maybe doing a full swap of a battery could be done like an f1 Pitstop.
Similar to those electric scooters in Asia, Just imagine if you rolled over a pitstop and had the battery quicky taken out from below the car and then a new battery placed back in.
That sort of system could change the economics of building an ev as you could move to a model where users don't really own the battery they rent it for a while until they need a swap.
Or electric cargo bicycles. Because every bike on the road is one less massive car.
Your first idea requires new, expensive infrastructure that will need maintenance due to mechanical parts. Given charging points are regularly broken at the moment, I don’t have high hopes. But even if we overcame that: it’s impractical in almost every major city in the World, because you’d have to drastically alter existing spaces, such as filling stations.
This might work in your context, and many others. It might even work for the “average” use case. But for 75% of the developed World (where the EV market is the fastest growing), I’m not convinced.
And the electric cargo bike argument - or bikes in general - work great for the “average” journey, but not many people actually take that journey.
My most frequent drive is 200+ miles in normally wet or cold weather. My next most frequent is 15+ miles in baking hot Summer sunshine in a heavily congested city where I need aircon. Neither would be pleasant on a bike - electric or not.
And I think that’s the point of this discussion: engineering for averages is a terrible idea, and most EVs don’t work for most journey profiles for most of the World’s drivers today, compared to ICE
Battery degradation would limit expectations. "Oh shit, I got one of those old batteries that will only get me 150 miles when I was hoping for 200 to get to my mother-in-law's for Thanksgiving" isn't going to work.
Then you are going to drive 150 miles and spend extra 3 mins to change the battery again - no? Not a big deal, and certainly not a deal breaker.
Nah - the pit-stop type battery replacement is the obvious solution to most EV charging problems, but we humans can not execute it. It requires level of coordination and cooperation between companies that we are not easily capable of right now.
Battery replacement works only if you make compromises. EVs are currently designed to put batteries where they fit, a standard battery means much less batteries and thus much less range. Second cars come in different sizes, a swappable battery needs to fit in the smallest car, leaving larger cars with a much to small battery.
Sure it can work, but overall I have to call it a bad compromise.
Could be solved by measuring how much charge it takes and bills you for that + some min charge for the change service would be the price, a bit more complex but I reckon the swap service could be made simple enough that it's low cost.
I don’t think this will ever happen. You will need to inventory $30,000 parts to sell them for $30,005 (if $5 is the cost of the charge). And the cars will have to have tons of design compromises.
I think the main mistake as concerns EVS (and many other environmental questions) is the belief that tomorrow will have exactly the same comforts as yesterday. If having to wait 45mn every 400km is the biggest price you’re paying for the carbon transition, you’re very lucky
Alternatively, the charging infrastructure needs to evolve. Even considering the currently available technology, imagine having 150kW chargers in place of every gas station that we have right now. Install ~20 chargers in the most busy locations, and the average time spent at the station will no be much higher than getting gas.
I thought this until I looked at the histogram of private car trip lengths. The vast majority of trips are very short. Its unlikely they're all being done on the same day.
Next time you have to bug out because there's a hurricane coming, and it's after your commute, so you haven't had time to charge the car, are you going to be regretting your choice? It's 95F out, humid, and your car AC is going full bore as you creep along in traffic to get out of the area.
Yes, that is not an average situation, but there's a lot of peace of mind not having to think about it at all. By the time I get down to 250 miles in my ICE, I can fill up in 5 minutes, but still have a very comfortable margin for anything that may happen.
And, worst case, if I run out of gas (never happened in my lifetime)? I can get a gallon of fuel and drive away. How does that work with an EV?
A reasonable US-specific problem. EV limitations like this are are why millions of people aren't currently interested in buying EVs. Compared to ICE, and EV car is more expensive, and essentially has the "road trip" feature removed.
There's a joke that goes something like "To an American 200 years is a long time, to a European 200km is a long distance".
Driving from San Diego to Sacramento is about 800km; in good weather and light traffic you could cover that in 7 or 8 hours. Get up early, drive that first leg, stop for lunch, then keep going (e.g. towards Portland or Seattle).
Of course, an American would usually stop for gas before hitting empty because we're used to the idea of "No food or fuel next 2 hours".
A couple of decades ago, when I was young(er) and (more) foolish, I several times did the drive between Columbia, SC and Dallas, TX in a single day. It was just a touch over a thousand miles. Idiocy.
I once did a whirlwind trip from TN to NM, UT, CO, and back to TN. 5,000+ miles in 5 days. Average speed over 40MPH with some sleep and some meetings included. Idiocy, indeed.
7 or 8 hours is a pretty long day driving for one person. But people do switch off and, even in New England where distances tend to be shorter, a 5 hour drive up to somewhere like Maine is hardly exceptional.
To bring up an issue relevant to Google and tech, this was my main criticism James Damore, and why I thought Google had grounds to fire him. The First Amendment gives him the right to write an incel-inspired manifesto if he wants to, but the misuse of "average" for political purposes makes him look like an idiot and discredits other work he might do. In his manifesto he argued that the average male is better suited to computer programming than the average female. How is that in any way relevant at Google, which only hires people 4 or 5 or 6 standard deviations away from the norm? Average isn't relevant. Bringing up the average in situations where the average is not relevant is a common mistake, but it is also a very stupid mistake.
Because certain people constantly use the fact that there isn't 50/50 gender representation in engineering roles as a way to imply the profession is particularly sexist. It was absolutely relevant to the conversation at hand around "women in stem".
> 4 or 5 or 6 standard deviations away from the norm
Assuming normal distribution:
Single tail 4s.d. is like 1 in 30k. There are about 300M people in the US. Doing the division, that's 10k people.
Google employs way more software engineers than that.
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Google does hire at the tail (just not as extreme as you claim). And when you select for the tail, slight difference in average translates to a huge gender imbalance.
Take height for example, we have quite some overlap between men and women. But when we select for people over 6', it's gonna be overwhelmingly men.
Even without the standard deviations I think averages are an often abused tool. If you take any statement following the lines of "group X is better at task then group Y on average", while it might help you win in the long term in a betting scenario it doesn't actually provide any information on whether any individual from group X is better at the task then any individual from group Y
> Openness directed towards feelings and aesthetics rather than ideas. Women generally also have a stronger interest in people rather than things, relative to men (also interpreted as empathizing vs. systemizing).
> These two differences in part explain why women relatively prefer jobs in social or artistic areas. More men may like coding because it requires systemizing and even within SWEs, comparatively more women work on front end, which deals with both people and aesthetics.
Not to split hairs, but that's a claim that the average degree of preference is higher among men, not that the average degree of being suited for it is higher among men.
The article is a short, low quality version of the previous several ones that were explaining in detail the history, the changes, the results. It does not belong here.
This reveals itself with the Carlin joke about the average person being dumb and that by implication 1/2 of the population is even dumber. Carlin and people who eagerly repeat it don’t know about distributions and that intelligence is not a standard distribution. Mea culpa, I used to parrot and believe the joke…
I suspect Carlin understood averages and the diversity of intelligence better than your comment implies. He probably was just having fun with the idea. After all, it is a good joke.
"standard normal distribution" is a normal distribution with mean 0 and s.d. 1.
To talk about whether intelligence follows a (one-dimensional) normal distribution we have to assign a number to it. That number is usually IQ, but by design the raw score is transformed to make IQ scores follow a normal distribution.
So it is trivially true.
If we want to go beyond that, what does it even mean to say, for example, "twice as smart"?
And in general people are really bad at thinking in term of distributions. If you discuss averages or percentiles, people identify to that metric like if it applied to every individual of that distribution. That makes the debate on D&I particularly unproductive.