You surely can’t be saying that that means the word “average” shouldn’t be used of it
Why, but I am saying this!
There must be a misunderstanding. “That”, in what I wrote, is the fact (kinda) that the median is a location parameter. This fact is also true of the mean. Therefore, “that” cannot be justification for not calling the median “average” unless it is also justification for not calling the mean “average”. But your whole argument is that the mean should be called “average” and the median shouldn’t.
Are you saying the word “average” means “a location parameter of a distribution”?
No (and I don’t really understand how you could get that idea from anything I wrote). I am saying:
The word “average” is used in a variety of ways. I’d much prefer to see it used much less, and more specific terms used instead.
When it is used with a specific meaning, it is (as you say) usually used to mean the arithmetic mean but (I say) it can also legitimately be used to mean other measures of central tendency.
One should say which one.
(I didn’t say this, but:) I don’t claim to have a precise definition of the characteristics a thing should have for it to be reasonable to call it an average. In practice, since children are taught in school—at least where I come from—that “the” “three” averages are the mean, the median and the mode, it is probably best to avoid the term for other kinds of average unless there’s an especially strong reason.
If you are being explicit, “median” is a perfectly fine word.
As I already said, in these exact words: I think it would be better if GWWC had said “median” rather than “average”. But the question isn’t whether “median” is a good word to use—we are agreed that it is—but whether “average” is a legitimate word to use. I say it is; you have offered no actual grounds for disagreeing with that. Do you disagree, or are you just arguing for the sake of arguing?
Yes, I think so. We seem to have persistent difficulties in being clear to each other.
Your line of reasoning looks to me like this: We can call small felines (mean) pussycats (average). The small felines are mammals (location parameters). Ninjas (medians) are also mammals. Therefore we can can call ninjas pussycats.
Do you disagree
Yes, and I thought I was pretty explicit about that:
Why, but I am saying this!
I wasn’t taught in school that there are three averages. To me “average” is a colloquial term for the mean with the implied handwaviness of “something something middle, we don’t care to specify precisely”. I do not think that that the word “average” should be used in the meaning of “median” (or “mode”).
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.
There must be a misunderstanding. “That”, in what I wrote, is the fact (kinda) that the median is a location parameter. This fact is also true of the mean. Therefore, “that” cannot be justification for not calling the median “average” unless it is also justification for not calling the mean “average”. But your whole argument is that the mean should be called “average” and the median shouldn’t.
No (and I don’t really understand how you could get that idea from anything I wrote). I am saying:
The word “average” is used in a variety of ways. I’d much prefer to see it used much less, and more specific terms used instead.
When it is used with a specific meaning, it is (as you say) usually used to mean the arithmetic mean but (I say) it can also legitimately be used to mean other measures of central tendency.
One should say which one.
(I didn’t say this, but:) I don’t claim to have a precise definition of the characteristics a thing should have for it to be reasonable to call it an average. In practice, since children are taught in school—at least where I come from—that “the” “three” averages are the mean, the median and the mode, it is probably best to avoid the term for other kinds of average unless there’s an especially strong reason.
As I already said, in these exact words: I think it would be better if GWWC had said “median” rather than “average”. But the question isn’t whether “median” is a good word to use—we are agreed that it is—but whether “average” is a legitimate word to use. I say it is; you have offered no actual grounds for disagreeing with that. Do you disagree, or are you just arguing for the sake of arguing?
Yes, I think so. We seem to have persistent difficulties in being clear to each other.
Your line of reasoning looks to me like this: We can call small felines (mean) pussycats (average). The small felines are mammals (location parameters). Ninjas (medians) are also mammals. Therefore we can can call ninjas pussycats.
Yes, and I thought I was pretty explicit about that:
I wasn’t taught in school that there are three averages. To me “average” is a colloquial term for the mean with the implied handwaviness of “something something middle, we don’t care to specify precisely”. I do not think that that the word “average” should be used in the meaning of “median” (or “mode”).
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.