What's it(s) mean?

[j4]

I asked AQA: "What's the average length of time for which UK jobs at AQA are advertised on the website? i.e. How long does it take for all/any positions to be filled? Thanks!"

AQA replied: "There's no average length of time, it just depends on the number of vacancies and the response. AQA advises applying immediately when they're advertised."

Now, call me a pedant, but I don't believe it's technically true that there's "no average length of time". I can entirely believe that they don't set a maximum or minimum length of time, and/or that they just don't want to tell me, but that's an entirely different kettle of question marks.

Comments

[simont]

In fact, there do exist probability distributions without any (finite) average. Suppose, for example, that there were a 1/2 chance of the job staying up for one day, a 1/4 chance of it staying up for two, a 1/8 chance of it staying up for four, and in general a 1/2ⁿ⁺¹ chance of it staying up for 2ⁿ days for all integer n ≥ 0. If you try to work out the expected average length of time for one to stay there, you'll find you end up with infinity – and yet it's a perfectly meaningful probability distribution.

Not that I'm suggesting that AQA's job adverts do in fact follow this pattern or anything like it, but it is at least possible in theory :-)

[cartesiandaemon.livejournal.com]

Ooh, good answer.

Wait, no the hell! There have been a finite number of jobs advertised, right? You must be able to average *those*.

Besides, yours has a perfectly good mode and median :) That was the tack I was going to take. If the distribution is exceptionally unusual, it's possible summing it up in any single figure wouldn't represent it at all well, and hence while any given sort of average *existed*, it wouldn't be an answer to the question "what's the average amount of time".

However, anyone actually trying to give information to J4 would be able to say "A large minority are filled immediately, the rest generally languish for a month or more" or whatever describes the situation.

The fact that they don't suggests they don't know or don't care or think it detrimental to do anything other than say "Go! Apply! Roll over! Beg! Apply as fast as possible"...

[simont]

There have been a finite number of jobs advertised, right? You must be able to average *those*.

Well, sure, but that's only a statistical sample and its mean will be at best an approximation to the mean of the real distribution. In this case, a very bad approximation!

Besides, yours has a perfectly good mode and median :)

That is true. I could at least have arranged for it to be bimodal. However, it's rather difficult to avoid having a median...

[cartesiandaemon.livejournal.com]

Well, sure, but that's only a statistical sample and its mean will be at best an approximation to the mean of the real distribution. In this case, a very bad approximation!

Hmmm. I guess it's possible they could deduce what distribution it was, and fill in the parameters from the data. But then surely anyone would send the formula? I assumed the original question was implicitly statistical in nature...

That is true. I could at least have arranged for it to be bimodal. However, it's rather difficult to avoid having a median...

Yeah... "Well, this week, two jobs were placed in time Δ, one in time ♣, one only after , and three had already been advertised for ⇑ months and remained unfilled, for a total median waiting time of E_INCOMPARABLE..." :)

[imc.livejournal.com]

The fact that they don't suggests they don't know or don't care or think it detrimental to do anything other than say "Go! Apply! Roll over! Beg! Apply as fast as possible"

I expect it was answered by an individual who doesn't know the answer and that it therefore doesn't suggest anything about their corporate attitude. However, if the question was sent to a recruitment or management address then it does indicate they have sloppy procedures.

On the other hand, if the question was sent to the usual text number (or via the "ask a free question" page) then it doesn't entirely surprise me that a precise answer was not forthcoming, because those questions go to people who aren't involved in recruitment or company management. A case of "you got what you asked for", although not literally, obviously.

I do tend to think that AQA's advertising makes a lot of promises that they can't actually keep.

[arnhem.livejournal.com]

Wait, no the hell! There have been a finite number of jobs advertised, right? You must be able to average *those*.

It'd be stunningly misleading to only average those for which you know the correct value, and if you set the "value" of those still open to "how long they've been open so far", that would be similarly very misleading (since that set will tend, for some distributions, to be skewed towards those that will remain open for a very long time indeed).

[cartesiandaemon.livejournal.com]

Oh, I'm sorry. I didn't actually think through what calculation was right, merely that you stand a fair chance of getting a finite answer. I think, I meant average amongst those, or "apply to those a process producing an average", rather than "MWAHAHAHAHAH I AM AN AVERAGING MONKEY GIVE ME ANY NUMBERS AND I'LL ADD THEM UP AND DIVIDE BY N HAHAHA".

I think *why* I forgot was probably being a mathematician, not a statistician and instinctively solving the case where there's an effectively infinite number, so the special case at the end is insignificant.

[j4.livejournal.com]

Do you mean I should have specified more clearly that I was asking for statistical data on the adverts which had already been posted and taken down, rather than probabilistic data on all adverts which might be posted in the future?

I wonder if there is a market for a pedant's Questions Answered service, where SWITCH NOBOYDIE is never assumed, and a carelessly phrased question can result in entirely the wrong answer. It would be a lot of fun to work for, if nothing else.

[cartesiandaemon.livejournal.com]

Do you mean I should have specified more clearly that I was asking for statistical data on the adverts which had already been posted and taken down, rather than probabilistic data on all adverts which might be posted in the future?

Oh good. *I* thought that's what you *were* asking, but I wasn't 100% sure. But someone sufficiently pedantic to take the other interpretation would surely never say "there is no average" without being more specific; even if they were entirely correct they would no doubt be unable to keep themselves from exhibiting an example distribution, even if not the real one :)

Ooh, no, I have it. There must be only one legitimate interpretation of the sentence, and he's challenged us to find it. Like the FAQ said, if he can't answer he'll provide an interesting nugget...

pedant's Questions Answered service

I think it would be eminently entertaining. Asking your friends list will probably have the desired result, of course :)