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"I have a ball"
"So you have a red ball?"
"No, it's green"
"If you don't specify then the statement needs to hold for all balls to be correct."And by the way: for the given plot, it is correct for all averages
More like
"Balls are orange"
"That's wrong"
"Ah but basketballs are balls and they are orange, gotcha"
"No, you just said balls, that's too generic, if you meant basket balls you should have said basket balls."not all basketballs are orange
But the average basketball is
Who cares? Everyone understands the example anyway.
The comment said "below average", not "below averages"
Doesn't matter for the issue at hand, that's just a question of language relating to the example. A different example:
"A set always has a maximal element under the larger-than relation for numbers"
"That's wrong"
"Ah but any set of natural numbers has a maximal element, that is also a set, gotcha"
"No, you just said set, that's too generic, if you meant any set of natural numbers you should have said that.""You're as stubborn as my brother"
"But your younger brother isn't stubborn at all"
"I was talking about my older brother"The average is a generic concept covering multiple more specific concepts like mean and median. If you say something about the generic concept it should not depend on any properties of just one of the specific concepts, in order to hold generally.
Your brother is a term for a single person that is simply under-determined and could turn out to apply to either one, but not both. What you say about your brother should apply to the brother you mean, in order to hold.
I don't even understand what you mean. If it covers more than one concept that can contradict each other, how can you expect that it is true for all of them?
Take the set 1, 7, 10. When I say the average is 7, you can say "no, the mean is 6" and when I say the average is 6 you will answer "no, the median is 7"