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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.
The number of readings at each weight within this range were:
172; 7
173; 0
174; 6
175; 3
176; 9
177; 0
178; 15
179; 7
180; 20
181; 0
182; 15
183; 0
184; 8
185; 1
indicating that some weights, such as 177, 181, and 183 are likely
to be filtered out by some distortion in the instrument and appear as
some different reading.
Much of the world uses metric so I looked at the implications of a
kilograms to pounds retrofit that was tacked onto scales that had been
designed to read to the nearest kilogram. For one artificial case, with
input being a series of weights difffering by 0.05 kg (76.50, 76.55...);
assuming output rounded to nearest kilogram, then converted to lb by
dividing by 0.45 and then rounded to the nearest pound, the frequency of
weights is either zero or 20 within the range 171 to 187--
Weights with a frequency of 20 were 171, 173, 176, 178, 180, 182, 184 &
187 while
weights with a frequency of zero were 172, 174, 175, 177, 179, 181, 183,
185 & 186.
The gaps in the artificial readouts don't exactly match gaps in the
actual readout (177, 181 and 183 do but not 179) but both examples show
that a rock-solid digital readout to zero or more decimal places may not
be as reliable as it appears.
Yours truly, Dave Webster, Kentville
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