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.
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.
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.
BAS's comment to which I was responding obviously related to the general population, hence the same applies to my response.It would for a general population because the vast majority of people have 2 arms and 2 legs, giving a very tight distribution ....
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.... but if you were to sample say crocodile tamers you might find a much different distribution skewed towards fewer limbs.
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!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 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.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.
Same here - in my case an awful lot moreInteresting that it's turned to statistics which I do know a bit more about than lightbulbs.
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.It is a bit dishonest to use a crude mean like that without compensating for the distribution.
Agreed. It goes without saying that no sort of average, alone, is going to tell one about 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.
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).The arms and legs is a very good example of the danger of averages ...
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.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.
Probably very wiseBack to the immediate problem - I'm now rather disinclined to fit anything which needs the removal of the ceiling if it fails.
Exactly - again, unless 50% or more had (non-integer) numbers of arms less than 2.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.
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 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 realise that and agree - which was also the spirit of my initial response.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.
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