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[JohnW2]

Eh? Unless more than half of people have less than 2, or more than 2, arms/legs/eyes, then the median, as well as the mode, will inevitably be 2.

 

[ban-all-sheds]

.

 

[ConcreteCastle]

Interesting that it's turned to statistics which I do know a bit more about than lightbulbs.

There's surely a joke about statisticians changing a bulb in there but it's too early in the day.

It is a bit dishonest to use a crude mean like that without compensating for the distribution.

Neither median or modal lifespan would be a whole lot better than mean without accounting for the deviation from it. If for example you sampled 10 bulbs, 3 lasted a week, 3 lasted 5 years and the remaining 4 lasted 3 years you could still market them as lasting 3 years (both modal and median) without acknowledging that 30% won't last a week.

The weights example is apt but the difference is they can control for it before the cornflakes leave the factory, and reject those which fall outside their tolerance. You don't know the life of a bulb until it fails.

The arms and legs is a very good example of the danger of averages, and I wouldn't recommend trying to comfort someone who has just lost their wrist by telling them they still have an above average endowment of arms compared to the population as a whole.

I suppose you can't start putting standard deviations and distribution curves on the side of light fittings, but it would be more honest if they had to give a lifespan at which say 95% still worked. And interesting to see what this would be.


Back to the immediate problem - I'm now rather disinclined to fit anything which needs the removal of the ceiling if it fails.

Thanks!

 

[ConcreteCastle]

Eh? Unless more than half of people have less than 2, or more than 2, arms/legs/eyes, then the median, as well as the mode, will inevitably be 2.

It would for a general population because the vast majority of people have 2 arms and 2 legs, giving a very tight distribution, but if you were to sample say crocodile tamers you might find a much different distribution skewed towards fewer limbs.

You might still find that the modal or median crocodile tamer has 2 arms and 2 legs but it would be false to assume that this makes crocodile tamers as likely to have all their limbs as the general population.

 

[ban-all-sheds]

I wouldn't recommend trying to comfort someone who has just lost their wrist by telling them they still have an above average endowment of arms compared to the population as a whole.

Your right leg, I like. I like your right leg. A lovely leg for the role. That's what I said when I saw you come in. I said, "A lovely leg for the role". I've got nothing against your right leg. The trouble is – neither have you.​

 

[EFLImpudence]

It might be worth pointing out for our younger viewers that the role in question was that of Tarzan.

I suppose younger viewers will know Tarzan?

 

[JohnW2]

It would for a general population because the vast majority of people have 2 arms and 2 legs, giving a very tight distribution ....

BAS's comment to which I was responding obviously related to the general population, hence the same applies to my response.

... but if you were to sample say crocodile tamers you might find a much different distribution skewed towards fewer limbs.

Of course. However, my most recent comment still stands - that, even in that population, and by definition, the median could not be other than 2 unless 50% or more of that population had less than 2 limbs.

You might still find that the modal or median crocodile tamer has 2 arms and 2 legs but it would be false to assume that this makes crocodile tamers as likely to have all their limbs as the general population.

I'm sure that no-one would think otherwise but, as above, I feel sure that it was clear to everyone that BAS was talking about the number of limbs he had in relation to the 'average' of the general population - it's only you who has introduced the issue of sub-populations which are potentially highly non-representative of the general population!

Kind Regards, John

 

[ban-all-sheds]

BAS's comment to which I was responding obviously related to the general population, hence the same applies to my response.
Of course. However, my most recent comment still stands - that, even in that population, and by definition, the median could not be other than 2 unless 50% or more of that population had less than 2 limbs.

I was, mea culpa, thinking of a continuous distribution which ranges from 0 to 2, and therefore in which the median would have to be less than 2.

But of course it isn't continuous. And there may be instances of people with 3 arms or 3 legs. Pretty sure I've never heard of 3 eyes.

Even if we were to devise a scale whereby people with abnormalities or partial amputations were classified as having 1.6 legs, or 1.495729350346 arms, in any list of limb numbers in a sample 2 would be in the middle.

 

[JohnW2]

Interesting that it's turned to statistics which I do know a bit more about than lightbulbs.

Same here - in my case an awful lot more

It is a bit dishonest to use a crude mean like that without compensating for the distribution.

I'm not sure what "like that" you're talking about, but I think that, in the sort of context we're talking about (information for consumers on the life expectancy of products) it would be very unusual for means to be quotes, since they are so 'unhelpful'. It's the same problem as I described for human survival. Many/most survival curves (including those for humans and for most manufactured products like light bulbs) have a 'bathtub' shape, with high early failure rates followed by a long period of very low failure rate, then eventually a progressive increase in failures - so a mean of all of that is very unhelpful, telling one nothing much about either early or late failures. As I said before, a mean is only really appropriate if, for example, one wants to determine the 'replacement costs' over a period of time.

Neither median or modal lifespan would be a whole lot better than mean without accounting for the deviation from it. If for example you sampled 10 bulbs, 3 lasted a week, 3 lasted 5 years and the remaining 4 lasted 3 years you could still market them as lasting 3 years (both modal and median) without acknowledging that 30% won't last a week.

Agreed. It goes without saying that no sort of average, alone, is going to tell one about the distribution.

The arms and legs is a very good example of the danger of averages ...

I would say that it is a very good example of using the wrong sort of 'average'. In that situation, either median or mode would provide exactly the information one would usually need (and information which corresponded with common sense).

I suppose you can't start putting standard deviations and distribution curves on the side of light fittings, but it would be more honest if they had to give a lifespan at which say 95% still worked. And interesting to see what this would be.

That is, of course, conceptually similar to what is going on with the 'weights and measures' labelling (i.e. the 'e'), albeit the consumers are not exposed to the mathematical technicalities. Using the most common convention, if one buys something labelled 100ge, that implies that there is a 97.5% probability that the contents will be no less than 95g - still, perhaps, not a concept which the general public can necessarily get their heads around too easily, but probably about the best one can do with something which is inevitably probabilistic.

Because of the 'bathtub' curve, to quote a lifespan which 95% of products would achieve would probably be very unhelpful for products like lightbulbs (which have a relatively high very early failure rate). Indeed, maybe I'm unlucky, but I would guess that my experience is probably that around 5% fail in the first few days (if not 'DOA'!). If that is the case, then a truthful indication of the lifespan which 95% would achieve might only be, say, 50 hours - which would leave one totally unable to distinguish (on the basis of the quoted '95% lifespan') between ones for which 'most' would last around 1,000, 5,000, 10,000 or 25,000 hours.

Back to the immediate problem - I'm now rather disinclined to fit anything which needs the removal of the ceiling if it fails.

Probably very wise

Kind Regards, John

 

[JohnW2]

Even if we were to devise a scale whereby people with abnormalities or partial amputations were classified as having 1.6 legs, or 1.495729350346 arms, in any list of limb numbers in a sample 2 would be in the middle.

Exactly - again, unless 50% or more had (non-integer) numbers of arms less than 2.

 

[ban-all-sheds]

I would say that it is a very good example of using the wrong sort of 'average'. In that situation, either median or mode would provide exactly the information one would usually need (and information which corresponded with common sense).

For the avoidance of any doubt, my comment about having an above average number of legs was meant as a humorous illustration of exactly that point, and the danger of saying "average" when it can mean any of several things.


As an aside, if you ever want to explain "distribution" to someone, when you're next in an old building with stone steps, look at the shape of the wear profile on the treads - it's a normal distribution.

 

[JohnW2]

For the avoidance of any doubt, my comment about having an above average number of legs was meant as a humorous illustration of exactly that point, and the danger of saying "average" when it can mean any of several things.

I realise that and agree - which was also the spirit of my initial response.

Things have moved on a bit, but when I was at school, those (I presume the majority of people) who pursued mathematical studies only a far as 'O'-level/GCE (now GCSE) were probably not aware of any sort of average other than an arithmetic mean - so many 'knew no better'.

 

[ban-all-sheds]

TBH I don't remember median and mode at A level either. Apart from geometric mean AFAIR we were not exposed to anything other than the arithmetic mean which "everyone" understands as average. And I don't remember having the use of geometric mean explained.

Do bear in mind though, that I've never needed to use any form of statistical analysis in my working life, apart from grasping the concept of the central limit theorem/regression to the mean, so the passage of time since A level maths could mean that I don't remember these things because I don't remember them, not because they weren't taught.

But a little of the gale-force blast of statistics I weathered in my first year at uni stuck, so it's more likely that they weren't taught in my A-level course.

 

[JohnW2]

My maths A-level (and, indeed, S-Level, which then existed!) did include a token amount of "Statistics and Probability" (particularly the latter) and I have a feeling (can't remember for sure) that that probably included at least an awareness of the nature of most types of 'averages'. However, my daughters' maths GCSEs (around the turn of the century) included significant amounts of 'Statistics and Probability' (but, again, I can't remember what that included by way of 'averages').

In passing, my personal opinion is that medians are probably under-used, particularly given that they can, in some senses, be used fairly 'mindlessly' - in the case of fairly symmetrical distributions, mean and median are usually going to be much the same, so it doesn't much matter which one uses, but if the distribution is markedly non-symmetrical, then the median is likely to be more appropriate/meaningful than a mean (if either is appropriate). Using a median is therefore, in some senses, 'fail safe' - and it would be very unusual (if it ever happens) for a median to give a significantly more 'misleading' impression than did a mean..

 

[ConcreteCastle]

Turned into quite an interesting thread. I'm glad I'm not the only person who dredges up abstract academic nonsense while blundering through DIY stuff. Economics degree in my case which covered a lot of statistics.

I believe I covered mean, mode and median at A level however it's the kind of thing that doesn't sink in until you apply it.

From a consumer point of view I think I had (lazily) assumed that to make that claim some proportion of the bulbs would have to last that long. The mean can be very misleading!

The point about looking at a sub group (crocodile tamers) was that even using median or modal numbers could be very misleading because even if they are the same as the general population the distribution is likely different. This means that the probability of any individual crocodile tamer missing part of a limb are greater than for the general population. Which appears to make LEDs the crocodile tamers of the bulb world.