Your line of reasoning looks to me like this: [...]
No. I am not saying “We can call ninjas pussycats because they are mammals”. I am saying “The fact that ninjas are mammals is not a reason not to call them pussycats”. There are other reasons for not calling ninjas pussycats, and those (not the fact that ninjas are mammals) are why we shouldn’t call ninjas pussycats. Which is why I was puzzled that you wrote “In normal, even academic, speech, ‘pussycat’ means Felis catus. A ninja is a mammal (as is a dog or cat).” And you didn’t state any actual reasons for not calling ninjas pussycats.
I wasn’t taught in school that there are three averages.
Fair enough; I was and my 10-year-old daughter was. (For the avoidance of doubt, I am not saying ”… and therefore that is the correct usage” but ”… which tells us something about how the term is likely to be understood by generally informed readers without specialist knowledge of statistics”. Of course schools in different places may do different things.)
To me “average” is a colloquial term for the mean with the implied handwaviness [...]
Here’s the Shorter Oxford[1]. Its meaning I is an older but obscure one to do with shipping.
II transf.4 The determination of a medial estimate or arithmetic mean. [...] 5 The generally prevailing rate, degree, or amount; the ordinary standard; the arithmetic mean. [...]
(I promise the bits I have omitted don’t change the meaning or implications of what I quoted.) That word “medial”, as defined in the same dictionary, has the same double use: it can mean specifically “equal to the arithmetic mean” but can also mean “typical”, “central”, “kinda in the middle”, etc.
As a further indication of how the word is used casually by a mathematically literate writer, here’s an extract from Darrell Huff’s famous “How to lie with statistics”:
When you are told that something is an average you still don’t know very much about it unless you can find out which of the common kinds of average it is—mean, median or mode.
This sort of usage really isn’t uncommon, and it’s why I think saying “average” when you mean the median (or even, for nice unimodal distributions, the mode) is reasonable—at least if, as GWWC did, you say somewhere what sort of average you are using.
[1] For the avoidance of doubt: Not because I think dictionaries determine meanings, but because good dictionaries record actual usages; the SOED is a very good dictionary.
No. I am not saying “We can call ninjas pussycats because they are mammals”. I am saying “The fact that ninjas are mammals is not a reason not to call them pussycats”. There are other reasons for not calling ninjas pussycats, and those (not the fact that ninjas are mammals) are why we shouldn’t call ninjas pussycats. Which is why I was puzzled that you wrote “In normal, even academic, speech, ‘pussycat’ means Felis catus. A ninja is a mammal (as is a dog or cat).” And you didn’t state any actual reasons for not calling ninjas pussycats.
Fair enough; I was and my 10-year-old daughter was. (For the avoidance of doubt, I am not saying ”… and therefore that is the correct usage” but ”… which tells us something about how the term is likely to be understood by generally informed readers without specialist knowledge of statistics”. Of course schools in different places may do different things.)
Here’s the Shorter Oxford[1]. Its meaning I is an older but obscure one to do with shipping.
(I promise the bits I have omitted don’t change the meaning or implications of what I quoted.) That word “medial”, as defined in the same dictionary, has the same double use: it can mean specifically “equal to the arithmetic mean” but can also mean “typical”, “central”, “kinda in the middle”, etc.
As a further indication of how the word is used casually by a mathematically literate writer, here’s an extract from Darrell Huff’s famous “How to lie with statistics”:
This sort of usage really isn’t uncommon, and it’s why I think saying “average” when you mean the median (or even, for nice unimodal distributions, the mode) is reasonable—at least if, as GWWC did, you say somewhere what sort of average you are using.
[1] For the avoidance of doubt: Not because I think dictionaries determine meanings, but because good dictionaries record actual usages; the SOED is a very good dictionary.