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183, 1 [I sent this out last night from another cptr, but it seems not to have come through, so here it is again] Hi Dave and other weight watchers, You're trying to discover the supposed 'law' behind the scale's readout conversion but you're doing this inadequately, by testing it with a small-sized, imperfect set of weights. These are the actual distribution of Dave's mass on a limited number of days -- real values unknown initially. This doesn't sound promising, so the first thing is to have a look at what the sampled weight distribution looks like, graphically, to see what you can make out. This might be normally distributed ('bell curve') or skewed, or might be bi-variate (two peaks), e.g. if Dave periodically overeats then fasts to lose weight. Most likely with only 91 samples (not that many), it is going to look noisy, but when plotted, the result is actually quite striking and rather simple. The counts at all the even-numbered sample points (178, 180 etc) give a reasonable, normal-looking distribution of values centered on Dave = 180 lb, a bit skewed towards the low end. By contrast, the counts at all the odd-numbered samples (181, 183...) are relatively small and most are actually zero. So the scale appears to be counting in twos (almost). How do these things work? I don't know for bathroom scales, but it's likely that they follow a modern instrumentation balance with a digital readout. These work by either by measuring the resistance of a strain gauge or by measuring the output of an electromagnetic detector, both analog outputs. So an analog voltage output is converted to a digital output according to a built-in internal conversion algorithm (an approximation equation operating inside a chip) that corrects for the undoubted non-linearity of the measuring system. This then drives the meter you look at. Digital meters indicate to the most significant digit*, so Dave's thing ought to be able to indicate 180, 181, 182, etc and wouldn't count in twos. All analog devices are noisy and also drift. If the manufacturer allowed the measuring device to put out the raw output, Dave would see his weight flicker disconcertingly between neighboring values even though he's keeping still. What's presumably going on is that the scale is averaging over a few seconds to stabilize the reading, then the algorithm is rounding it to a specified intervals. I can imagine how it could round to the nearest two pounds, but that wouldn't explain how Dave had seven values at 179 (odd number). Maybe someone else can think what sort of algorithm could count, centred on twos, but slop over at the edges occasionally into ones*. Anyone else know the answer? Seems implausible that the algorithm would record the conversion in kg then convert this to lbs in such a clumsy way, such that rounding errors in the last conversion crept in, but I suppose you never know. Steve *come to think, specifications are usually rated to the nearest significant digit +1, so maybe that's something to do with what they are up to. On 3-Dec-06, at 5:19 PM, David & Alison Webster wrote: > Dear All, Dec 3, 2006 > There is, as usual, a lull in NatureNS traffic as we near winter > and this lull provides an opportunity to comment on something that I > found interesting; a digital readout with 'missing numbers'. > I have weighed myself on digital bathroom scales, that have > readout to the nearest pound, for about 255 sundays and readout spans > 192 to 168 lb. It soon became clear that some weights were favoured > relative to others. For example for the 91 weights on one page (May 4, > 2003 to Jan 23, 2004), the readings cover a range of 172 to 185 but > some intermediate weights were not represented. ... >
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