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I know people learn this in middle school, but I've never seen an actual scholarly work call the median or mode "the average"--and I think I'd find it slightly

I know people learn this in middle school, but I've never seen an actual scholarly work call the median or mode "the average"--and I think I'd find it slightly misleading if they did. "Typical", "likely", (etc) are all fine, but to me, "average" strongly implies "mean."

Laremere 5y ago
That precision of language is not the way most people would use that word, eg "a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values" - https://www.merriam-webster.com/dictionary/average https://www.merriam-webster.com/dictionary/average "be conservative in what you do, be liberal in what you accept from others" - Robustness principle It's good to be precise when communicating, but in most contexts you shouldn't expect it from others.
- mattkrause 5y ago
  I understand that some sources say that one can use "average" to mean something other than the mean. My claim, as an actual working[0] scientist who encounters those words a lot, is that nobody really does, outside of "Well, actually the average can be the median or mode too...."-type statements. I'd put describing the mode as "the average" on par with giving someone a tomato and zucchini salad while describing it as "mixed berries." Not technically wrong but.... [0] Well, slacking scientist at the moment, but...
- Nition 5y ago
  For the record I was assuming that "average" meant mean in my original comment.
sellyme 5y ago
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.
OJFord 5y ago
Whatever 'scholarly work' does or doesn't do, journalists certainly interchange them; sometimes leaving a hint like the implied distinction between 'the average <trait>' (mean) and 'the average person's <trait>' (median; sometimes mode for physical discrete things). Also, though, that can just be sloppy and have no intentional implication, misleading depending on the reader.

Laremere 5y ago

That precision of language is not the way most people would use that word, eg "a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values" - https://www.merriam-webster.com/dictionary/average https://www.merriam-webster.com/dictionary/average "be conservative in what you do, be liberal in what you accept from others" - Robustness principle It's good to be precise when communicating, but in most contexts you shouldn't expect it from others.

mattkrause 5y ago
I understand that some sources say that one can use "average" to mean something other than the mean. My claim, as an actual working[0] scientist who encounters those words a lot, is that nobody really does, outside of "Well, actually the average can be the median or mode too...."-type statements. I'd put describing the mode as "the average" on par with giving someone a tomato and zucchini salad while describing it as "mixed berries." Not technically wrong but.... [0] Well, slacking scientist at the moment, but...
Nition 5y ago
For the record I was assuming that "average" meant mean in my original comment.

sellyme 5y ago

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.

OJFord 5y ago

Whatever 'scholarly work' does or doesn't do, journalists certainly interchange them; sometimes leaving a hint like the implied distinction between 'the average <trait>' (mean) and 'the average person's <trait>' (median; sometimes mode for physical discrete things). Also, though, that can just be sloppy and have no intentional implication, misleading depending on the reader.