[NatureNS] Digital measurements

Date: Sun, 03 Dec 2006 17:19:24 -0400
From: David & Alison Webster <dwebster@glinx.com>
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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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