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Scholarly works will pretty much never call the mean "the average" without clarifying what they mean either. As for the implication, a statement along the line

Scholarly works will pretty much never call the mean "the average" without clarifying what they mean either. As for the implication, a statement along the lines of "the average person" will almost always be interpreted as median, not mean. For example, Jeff Bezos lives in Medina, WA, a remarkably anagrammatic suburb for this demonstration. You can probably understand why saying "the average person in Medina has a net worth of $65,000,000" is both somewhat misleading and remarkably unhelpful for pretty much any purpose you'd want that information.

mattkrause 5y ago
People use "mean" and "average" in way that suggest they're the same, but one certainly doesn't have to say "average (herein defined as the mean)" because that's the overwhelmingly dominant meaning anyway. Two random examples from other tabs I had open: https://direct.mit.edu/neco/article/16/3/477/6879/Mean-Instantaneous-Firing-Frequency-Is-Always https://direct.mit.edu/neco/article/16/3/477/6879/Mean-Insta... or https://www.cell.com/neuron/fulltext/S0896-6273(13)00798-8 https://www.cell.com/neuron/fulltext/S0896-6273(13)00798-8 Mean and average are clearly the same thing, but only via context. In fact, I'd say that "averagING" (as a verb) almost has to be the mean; I'd find it deceptive if it were mode-finding. You're right that people often conflate the mean and median, but I think that's more to do with underestimating the very, very long tails of some distributions.
- samatman 5y ago
  You're replying to a perfectly clear demonstration that people often mean the median when they say average, and completely ignoring it. What was the point of that?
  - mattkrause 5y ago
    That it's rarely deliberate. I certainly agree that people mix them up. If you ask someone to quickly estimate the average/mean of something, you are likely to get some other location measure, like the median or mode. Some of this might be a heuristic: it's easier to mentally estimate the middle/most common item than it is to keep a running sum, and for many distributions, you get a similar answer. Some of it might be due to fogginess over the definitions. And, of course, these other summary statistics are often closer to what people regard as a `typical' value, especially if there's a long tail, so it On the other hand, suppose we had some data like this X=[2, 2, 2, 4, 4, 8, 16] If I asked you what the average of X was, the answer I'm expecting is "5.4", or perhaps "the median is 4", "the mode is 2", etc. I would be surprised if you just answered "2" or "4", and once I figured out what you did, I would find it annoyingly pedantic. I've worked with a lot of different people from different backgrounds, and I don't think anyone has ever used (unadorned) average to mean something other than the mean. Perhaps your experience is different.
    - samatman 5y ago
      Ah. Alright, this is rooted in a confusion between the normal use in statistics and the normal use in human speech. Absolutely, average-without-qualifications means the mean, if we're going to be handed a list of actual numbers and expected to produce another number from them. But especially for highly right-tailed distributions, when people talk about the average, they mean something more like the median, if there's a significant difference. I would find it annoyingly pedantic if someone said the average net worth in Jeff Bezos' municipality was 60mm, if the median was closer to 0.75mm. If I was handing someone an Excel spreadsheet of tax returns, I would of course tell them that we needed the median. Or the mean but in this circumstance I wouldn't use the word 'average' because of the wide skew. If I did anyway, yeah I would probably get the mean back. That's how average works in statistics, but not in common speech.

mattkrause 5y ago

People use "mean" and "average" in way that suggest they're the same, but one certainly doesn't have to say "average (herein defined as the mean)" because that's the overwhelmingly dominant meaning anyway. Two random examples from other tabs I had open: https://direct.mit.edu/neco/article/16/3/477/6879/Mean-Instantaneous-Firing-Frequency-Is-Always https://direct.mit.edu/neco/article/16/3/477/6879/Mean-Insta... or https://www.cell.com/neuron/fulltext/S0896-6273(13)00798-8 https://www.cell.com/neuron/fulltext/S0896-6273(13)00798-8 Mean and average are clearly the same thing, but only via context. In fact, I'd say that "averagING" (as a verb) almost has to be the mean; I'd find it deceptive if it were mode-finding. You're right that people often conflate the mean and median, but I think that's more to do with underestimating the very, very long tails of some distributions.

samatman 5y ago
You're replying to a perfectly clear demonstration that people often mean the median when they say average, and completely ignoring it. What was the point of that?
- mattkrause 5y ago
  That it's rarely deliberate. I certainly agree that people mix them up. If you ask someone to quickly estimate the average/mean of something, you are likely to get some other location measure, like the median or mode. Some of this might be a heuristic: it's easier to mentally estimate the middle/most common item than it is to keep a running sum, and for many distributions, you get a similar answer. Some of it might be due to fogginess over the definitions. And, of course, these other summary statistics are often closer to what people regard as a `typical' value, especially if there's a long tail, so it On the other hand, suppose we had some data like this X=[2, 2, 2, 4, 4, 8, 16] If I asked you what the average of X was, the answer I'm expecting is "5.4", or perhaps "the median is 4", "the mode is 2", etc. I would be surprised if you just answered "2" or "4", and once I figured out what you did, I would find it annoyingly pedantic. I've worked with a lot of different people from different backgrounds, and I don't think anyone has ever used (unadorned) average to mean something other than the mean. Perhaps your experience is different.
  - samatman 5y ago
    Ah. Alright, this is rooted in a confusion between the normal use in statistics and the normal use in human speech. Absolutely, average-without-qualifications means the mean, if we're going to be handed a list of actual numbers and expected to produce another number from them. But especially for highly right-tailed distributions, when people talk about the average, they mean something more like the median, if there's a significant difference. I would find it annoyingly pedantic if someone said the average net worth in Jeff Bezos' municipality was 60mm, if the median was closer to 0.75mm. If I was handing someone an Excel spreadsheet of tax returns, I would of course tell them that we needed the median. Or the mean but in this circumstance I wouldn't use the word 'average' because of the wide skew. If I did anyway, yeah I would probably get the mean back. That's how average works in statistics, but not in common speech.