To be honest, I think that the stronger argument is that "average" has different meanings, only one of which is "arithmetic mean," and that "arithmetic mean" is not the most common colloquial meaning. Hence when someone says "average," the assumption that they mean "arithmetic mean" is an invalid assumption, and likely to lead to errors in interpreting their statements. That being said, you raise a couple of fair points.
That's a fair point. However, the argument that mean ~ median puts the cart in front of the horse. Why not just calculate a median in the first place? Then at least you don't care about the distribution. It also lends itself well towards quartile/percentile information, which is quite interesting for some topics (i.e. wealth distribution).
Because you complained that "average" implies mean, and that the mean does not represent a point where half are above and half are below. However, in a normal distribution, which is a distribution that is often used to model natural phenomena (rightly or wrongly), the mean is the median, hence the distinction is irrelevant. Since normality is normally assumed (especially colloquially), it is entirely appropriate to say that half of data points are below the mean unless (a) the discussion is of a more technical nature (i.e. not colloquial English) or (b) we specifically state a priori that we are not dealing with a normal population.
Moreover, the median is a difficult statistic to come to terms with through sampling. For instance (if I recall correctly) the sample median is not an unbiased estimator of the population median, while the sample mean is an unbiased estimator of the population mean. The sample mean also converges pretty quickly to the population mean as the sample size increases. While the median is often a more accurate measure of center, it requires very large samples (or a census) in order to get a good estimate of it. Hence the mean is generally used.
Variable independence aside, I believe you're making assumptions that the central limit theorem doesn't allow. It's possible that while there are thousands of observable attributes of lawyers, the only one that matters is "mojo". If one has mojo, he(she) wins cases and finds legal loopholes; and if one doesn't, one suck balls. Therefore, your assertion that overall lawyer quality must be something near a Gaussian is incorrect in a mojo-driven universe.
I explicitly stated that I was assuming that lawyer quality was a function of several variables, and that we had independence. If mojo is the only variable that matters, we lose that independence (as all other measured variables depend upon that mojo variable), and my argument fails. I explicitly stated that this was the case. When we make the assumptions that I made, the Central Limit Theorem does imply that lawyer quality should be roughly normally distributed.
Of course, even if mojo is the only variable that matters, we still have to come to terms with its distribution in the population. It could still be normal.
Again, my main point was to distinguish between a technical usage of "average" and a colloquial usage of the term. I stand by my statement, namely that the original poster was being a hypocrite, and that he was only correct in a technical sense, and not in a colloquial (or more general mathematical) context.
I find it odd that you have a signature proclaiming your hate of grammar nazis, then you post something like the above. Grammar nazis are people who are overly pedantic about the structure and syntax of language, while you are being overly pedantic about the use of a fairly common word, which happens to have many related meanings in colloquial usage. In colloquial English, an "average" is any measure of central tendency. Even in mathematics, "average" is a somewhat ambiguous term, and can refer to the arithmetic mean (the average that you provide an example of), the geometric mean (calculated similarly, but with some extra powers of 2 and a square root), higher order means, or a variety of other measures of center.
Additionally, even if the original poster meant the arithmetic mean, his statement was probably not that far off the mark. Yes, the arithmetic mean is not a resistant measure of center, and can be influenced dramatically by outliers. On the other hand, in a normally distributed set of data, the arithmetic mean and the median will be equal. In many populations, many of the statistics that you could measure will be (approximately) normally distributed. Hence about half of the population will be above the arithmetic mean, and about half will be below. Since a metric which quantifies the quality of a lawyer is likely to consist of many variables, each with their own distributions, the central limit theorem implies that the overall distribution of quality will be normal (of course, this is under the assumption that a large enough proportion of those variables are independent, which may or may not be a dubious assumption). Basically, the quality of lawyers is probably a (more or less) normally distributed random variable, and about half of lawyers are less than average (i.e. of a quality lower than the mean).
In short, you (a) are being a math nazi, which strikes me as hypocritical, given your stance on grammar nazis; and (b) are only correct in a technical sense, and not in a colloquial (or even general mathematical) sense.
If you are that concerned about the security of your data, then you either encrypt all of your data, in which case it probably doesn't matter what happens to the drive after you get rid of it; or you destroy the drive and suck up the cost of a new one (or you are a large customer, and have an agreement with the vendor which allows you to destroy the drive and get a replacement). Security, convenience, or low cost---pick one.
I have a BA in mathematics. My school offered as BS track as well. The only difference was the foreign language requirement: the BA required four semesters (or equivalent) of a foreign language, while the BS dropped that requirement in favor of a two semester CS sequence (basically, introduction to programming and algorithms). From other institutions, the distinction might be more profound, but the basic moral of the story is that anyone making a decision on the basis of BA vs BS is a moron. If they were smart, they would read the applicant's transcripts.
In the essay linked in this post, the author specifically discusses the distinction between training and education. Perhaps you should [re]read that section?
While I do think that higher education is valuable, this isn't always reflected in pure economic terms. If you are going to make an economic argument, surely you are familiar with the term "sunk costs?"
Parse that last sentence again. Gawker had at least one vulnerability that they did not know about. One or more black hats found that vulnerability, and exploited it. In the same situation, white hats would have found the vulnerability and reported it. They were relying on the goodwill of white hats to report errors, rather than being more proactive themselves, and got pwned. This is, they say, embarrassing, and a situation that they should not have been in.
microbes (hell, even complex multi cellular organisms) THRIVE under incredibly hostile conditions right here on this planet. but it's "impossible" organisms eat arsenic because it's "poison"
You are missing the point. No one has said that life in an arsenic-rich environment is impossible. No one said that life could not exist without phosphorus. What the critics are saying is that the paper published in Science does not adequately demonstrate that life the bacteria under study can use arsenic instead of phosphorus (which was the conclusion of the original paper). There are at least two problems with the procedure, as published in Science.
Yeah, it's an extraordinary claim, I guess we should just get used to this sort of reaction whenever something game changing is claimed.
The process has always worked this way. The only difference is that we now have the television, radio, email, and other means of near-instantaneous communication, which allows the drama to play out in public, rather than in academic journals.
There is no "is" in science. Everything is in terms of "maybes." This reflects the epistemological position that nothing in science is certain, but that things can be more or less likely based upon the preponderance of evidence. In this case, the samples may not have been properly washed (the original paper leaves out those details), and if the samples were not properly washed, there is an obvious source of contamination. The correct response is not to attacked Dr. Redfield for disagreeing with the paper, but for Wolfe-Simon et al. to clarify how the experiment was run, and to demonstrate that Dr. Redfield's critique is invalid.
The cases are not comparable. Handel lived in an era when the patronage system was still in place---he was, for all intents and purposes, employed as a musician. He was supported by the wealthy with the understanding that he would create new works. In essence, Handel was paid in advance. This contrasts with many later artists, Poe included, who were paid after publication. Handel was not greatly harmed if his works were copied---his patrons had already paid him. Poe was harmed if his works were copied---he was not paid for those copies.
ven so, there should be a recognition that one has done the work before. You might forget what the formula is, or how to solve a certain kind of problem, but to utterly fail to recognize that you have ever seen such a problem before is stunning. I may not remember L'Hopital's rule. I may not remember even the name of L'Hopital's rule. But if I encounter limit of the form f(x)/g(x), I am going to remember that there was a way for working with those, and pull out my Calculus I text (or run to Wikipedia, or my nearest math department).
The problem here is not that the doctor reinvented the wheel, but that he was so incompetent that he did not even know that the wheel had been invented, nor did he know that he had seen it before, nor did he even have the insight to find an expert in the field for help.
Was, not is, a loss leader. At the time that Toyota first started producing the Prius, it was a loss leader. Now they have the technology in more vehicles, and the price of making hybrids has come down. My understanding is that the Prius has been profitable for several years now.
Not to mention the fact that the Prius was a loss-leader. People who were in the general Prius demographic but couldn't afford one (or who wanted more leg room, or more seats, or something else) were lured to Toyota lots, and ended up driving off with Corollas or Camries, which do make money.
How is this any different from the rest of a dead person's estate? When a person dies, there is always the potential that their heirs will argue about the disbursement of the estate, and that scandals will come to light. The dead person is dead. By definition, they don't care. It is the right of the heirs (either those selected by the deceased, or those determined by the courts) to determine what to do with the estate.
The people who are buying Wiis clearly disagree with your assessment. Is it possible that you are not the intended audience of the Wii? and that the audience that Nintendo is actually trying to court is quite happy?
Slashdot Mirror
I'm a math guy, and I think that I am missing something. Is that a physics joke?
To be honest, I think that the stronger argument is that "average" has different meanings, only one of which is "arithmetic mean," and that "arithmetic mean" is not the most common colloquial meaning. Hence when someone says "average," the assumption that they mean "arithmetic mean" is an invalid assumption, and likely to lead to errors in interpreting their statements. That being said, you raise a couple of fair points.
Because you complained that "average" implies mean, and that the mean does not represent a point where half are above and half are below. However, in a normal distribution, which is a distribution that is often used to model natural phenomena (rightly or wrongly), the mean is the median, hence the distinction is irrelevant. Since normality is normally assumed (especially colloquially), it is entirely appropriate to say that half of data points are below the mean unless (a) the discussion is of a more technical nature (i.e. not colloquial English) or (b) we specifically state a priori that we are not dealing with a normal population.
Moreover, the median is a difficult statistic to come to terms with through sampling. For instance (if I recall correctly) the sample median is not an unbiased estimator of the population median, while the sample mean is an unbiased estimator of the population mean. The sample mean also converges pretty quickly to the population mean as the sample size increases. While the median is often a more accurate measure of center, it requires very large samples (or a census) in order to get a good estimate of it. Hence the mean is generally used.
I explicitly stated that I was assuming that lawyer quality was a function of several variables, and that we had independence. If mojo is the only variable that matters, we lose that independence (as all other measured variables depend upon that mojo variable), and my argument fails. I explicitly stated that this was the case. When we make the assumptions that I made, the Central Limit Theorem does imply that lawyer quality should be roughly normally distributed.
Of course, even if mojo is the only variable that matters, we still have to come to terms with its distribution in the population. It could still be normal.
Again, my main point was to distinguish between a technical usage of "average" and a colloquial usage of the term. I stand by my statement, namely that the original poster was being a hypocrite, and that he was only correct in a technical sense, and not in a colloquial (or more general mathematical) context.
Or perhaps d(work(t))/dt. This seems like a situation where the function should be defined in terms of time. ;)
I find it odd that you have a signature proclaiming your hate of grammar nazis, then you post something like the above. Grammar nazis are people who are overly pedantic about the structure and syntax of language, while you are being overly pedantic about the use of a fairly common word, which happens to have many related meanings in colloquial usage. In colloquial English, an "average" is any measure of central tendency. Even in mathematics, "average" is a somewhat ambiguous term, and can refer to the arithmetic mean (the average that you provide an example of), the geometric mean (calculated similarly, but with some extra powers of 2 and a square root), higher order means, or a variety of other measures of center.
Additionally, even if the original poster meant the arithmetic mean, his statement was probably not that far off the mark. Yes, the arithmetic mean is not a resistant measure of center, and can be influenced dramatically by outliers. On the other hand, in a normally distributed set of data, the arithmetic mean and the median will be equal. In many populations, many of the statistics that you could measure will be (approximately) normally distributed. Hence about half of the population will be above the arithmetic mean, and about half will be below. Since a metric which quantifies the quality of a lawyer is likely to consist of many variables, each with their own distributions, the central limit theorem implies that the overall distribution of quality will be normal (of course, this is under the assumption that a large enough proportion of those variables are independent, which may or may not be a dubious assumption). Basically, the quality of lawyers is probably a (more or less) normally distributed random variable, and about half of lawyers are less than average (i.e. of a quality lower than the mean).
In short, you (a) are being a math nazi, which strikes me as hypocritical, given your stance on grammar nazis; and (b) are only correct in a technical sense, and not in a colloquial (or even general mathematical) sense.
Not to mention that he stated that the habit developed when he was a child, and likely had no control over the thermostat.
If you are that concerned about the security of your data, then you either encrypt all of your data, in which case it probably doesn't matter what happens to the drive after you get rid of it; or you destroy the drive and suck up the cost of a new one (or you are a large customer, and have an agreement with the vendor which allows you to destroy the drive and get a replacement). Security, convenience, or low cost---pick one.
No true Scotsman, eh?
I teach college students who are unfamiliar with that meme. Thank you for making me feel not so old again. :\
I have a BA in mathematics. My school offered as BS track as well. The only difference was the foreign language requirement: the BA required four semesters (or equivalent) of a foreign language, while the BS dropped that requirement in favor of a two semester CS sequence (basically, introduction to programming and algorithms). From other institutions, the distinction might be more profound, but the basic moral of the story is that anyone making a decision on the basis of BA vs BS is a moron. If they were smart, they would read the applicant's transcripts.
In the essay linked in this post, the author specifically discusses the distinction between training and education. Perhaps you should [re]read that section?
While I do think that higher education is valuable, this isn't always reflected in pure economic terms. If you are going to make an economic argument, surely you are familiar with the term "sunk costs?"
Parse that last sentence again. Gawker had at least one vulnerability that they did not know about. One or more black hats found that vulnerability, and exploited it. In the same situation, white hats would have found the vulnerability and reported it. They were relying on the goodwill of white hats to report errors, rather than being more proactive themselves, and got pwned. This is, they say, embarrassing, and a situation that they should not have been in.
You are missing the point. No one has said that life in an arsenic-rich environment is impossible. No one said that life could not exist without phosphorus. What the critics are saying is that the paper published in Science does not adequately demonstrate that life the bacteria under study can use arsenic instead of phosphorus (which was the conclusion of the original paper). There are at least two problems with the procedure, as published in Science.
Except that your depiction of the debate is incorrect. In reality, it looks more like this:
Wolfe-Simon et al.: We have made an extraordinary claim!
Redfield et al.: Your methods appear to be flawed.
And that is as far as we have gotten. In other words, the process is working.
The process has always worked this way. The only difference is that we now have the television, radio, email, and other means of near-instantaneous communication, which allows the drama to play out in public, rather than in academic journals.
There is no "is" in science. Everything is in terms of "maybes." This reflects the epistemological position that nothing in science is certain, but that things can be more or less likely based upon the preponderance of evidence. In this case, the samples may not have been properly washed (the original paper leaves out those details), and if the samples were not properly washed, there is an obvious source of contamination. The correct response is not to attacked Dr. Redfield for disagreeing with the paper, but for Wolfe-Simon et al. to clarify how the experiment was run, and to demonstrate that Dr. Redfield's critique is invalid.
The cases are not comparable. Handel lived in an era when the patronage system was still in place---he was, for all intents and purposes, employed as a musician. He was supported by the wealthy with the understanding that he would create new works. In essence, Handel was paid in advance. This contrasts with many later artists, Poe included, who were paid after publication. Handel was not greatly harmed if his works were copied---his patrons had already paid him. Poe was harmed if his works were copied---he was not paid for those copies.
ven so, there should be a recognition that one has done the work before. You might forget what the formula is, or how to solve a certain kind of problem, but to utterly fail to recognize that you have ever seen such a problem before is stunning. I may not remember L'Hopital's rule. I may not remember even the name of L'Hopital's rule. But if I encounter limit of the form f(x)/g(x), I am going to remember that there was a way for working with those, and pull out my Calculus I text (or run to Wikipedia, or my nearest math department).
The problem here is not that the doctor reinvented the wheel, but that he was so incompetent that he did not even know that the wheel had been invented, nor did he know that he had seen it before, nor did he even have the insight to find an expert in the field for help.
I'm still going to say the same thing, but I am going to publish it as "Henderson's Axiom."
Was, not is, a loss leader. At the time that Toyota first started producing the Prius, it was a loss leader. Now they have the technology in more vehicles, and the price of making hybrids has come down. My understanding is that the Prius has been profitable for several years now.
Not to mention the fact that the Prius was a loss-leader. People who were in the general Prius demographic but couldn't afford one (or who wanted more leg room, or more seats, or something else) were lured to Toyota lots, and ended up driving off with Corollas or Camries, which do make money.
How is this any different from the rest of a dead person's estate? When a person dies, there is always the potential that their heirs will argue about the disbursement of the estate, and that scandals will come to light. The dead person is dead. By definition, they don't care. It is the right of the heirs (either those selected by the deceased, or those determined by the courts) to determine what to do with the estate.
The people who are buying Wiis clearly disagree with your assessment. Is it possible that you are not the intended audience of the Wii? and that the audience that Nintendo is actually trying to court is quite happy?
Ahem... 7.25.
Wait... that's a possibility? Well, then... I think we need to get moving on this "mine the belt" idea right away!