You idiot. In other words, you're simply going to avoid the topic, because you have no argument. I'm well aware of the assumptions, I've even expounded on some of them for you. And you're right, you're analogy is absolutely useless. Nobody who knows anything about statistics actually believes that there are people out there with 1.5 cars, and 2.4 children. More to the point, have you read your own source? the argument comes down to this: Which i've already stated I agree with, but don't think is neccessarily relevant. In short, that paper raises many of the things that i've already mentioned, even some of the concerns i've expressed (not neccessarily to you, but that's whta you get for making assumptions), and as far as the deomstration with the coffee and the iced water goes, all that really demonstrates is the importance of choosing the correct statistic. I would also argue that that particular example is a really bad example, because how you define the system is also critically important. That example compeltely ignores the room, and only looks at the various averages of the two cups, when anyone with two braincells to rub together (which, admittedly might exclude you) can see that the cups aren't reaching equilibrium with each other, but they're reaching equilibrium with the room, and the averages of the cups are not representative of the averages of the system. So they've looked at bad measures, and compared bad measure to good measures, and they've poorly defined the system that they're taken the averages of, and on the basis of those bad choices, come to the conclusion that the original idea is meaningless. Anybody who's actually studied statistics knows that not all measures of the center of the data are equally valid for all systems. Some can give false impressions and indicate false trends. That's the simple fact that you seem to have lost site of - is that an average is 'simply' a measurement of the center point of the data. To use their example, the Harmonic mean of the temperature of the two cups is genuinely pretty much meaningless. The temperature at a location on the earths surface tends to pretty much follow a normal curve, but the harmonic mean is really only useful in a log normal distribution. The Harmonic mean is calculated by taking the nth root of the product of the individual data points (nothing to do with sums at all). This is equivalent, however to taking the average of the logs of the data points, but this is only useful when dealing with something that varies over several orders of magnitude, which temperature doesn't. So saying that because the harmonic mean decreases while the simple mean decreases the idea of applying a mean to temperature is meaningles, is quite simply, a logical fallacy (in part because no sane statistician would try and apply a harmonic mean to temperature, because it's the wrong mean to use). Something similar can be said for the Root Mean Square, which is calculated by squaring the data points, taking their average, then taking the square root of that. RMS gets used where the simple average would be zero - for example, the simple average of the voltage in the mains line is 0 volts. Does that mean I think it's safe to shove a fork in the plug, because on average, there's no voltage in the lines, so surely it must be safe. So again, they've used the wrong measure, and claimed because it disagrees, the idea of a mean temperature is wrong. They say it's precedented, but that doesn't mean it's appropriate.