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.
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.
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
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.