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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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