Threads here often do find tangents to pursue! For what it's worth, albeit not my primary discipline of professional education, in terms of statistical education I reckon I could probably 'trump' youTurned 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.
As I said, I think my A-level covered the concepts of most/all types of 'average', although little more than that. Computationally, there was not an awful lot that we could have realistically done in those days, since all we had were pens and paper, slide rules and log tables!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.
I'm not sure what "that claim" you are referring to, but, in relation to light bulbs etc., that is surely what is being done by making a 'claim' based on the median - the "some proportion" then being 50% - or am I misunderstanding you?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!
As I said before, because of the relatively high very early failure rate of light bulbs/lamps, if one goes for a much higher centile than the median (e.g. 95%) one is likely to end up with a very unhelpful figure - quite probably just a few hundred hours (at most), even if a very high proportion achieve at least 10,000. Similarly with a mean, since it would not take many very early failures to pull down the mean (which could be orders of magnitude greater) down to an unhelpful/'misleading figure'.
Indeed, but the same is true for the mean or any other 'average'. The problem with so many things (and light bulbs are a prize example) is the shape of the survival curve. No type of single overall 'average', or any other single overall statistic, will give any indication of how many early failures there may be at the same time as giving information about longer-term survival (in the majority). Similar to what you have said, the fact that bulbs lamps are sold with a (median-based) claim that 50% will last for, say, 10,000 years does not preclude the possibility that 49% will only survive for 5 minutes.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.
That problem could only be overcome by giving more, and more complex, information - but I'm not sure how realistic that would be in relation to the 'general public'. For me, short of giving me the actual failure/survival curves to look at, I think the most useful thing (assuming a roughly 'bathtub' curve) would probably be to give me two figures - one for 'very early failure rate' (e.g. the first 50 or 100 hours), and a separate figure which was some sort of average life expectancy for those which survived that initial period.
Kind Regards, John