[NatureNS] Digital measurements

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From: c.majka@ns.sympatico.ca
Date: Sun, 3 Dec 2006 19:51:11 -0400
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Hi Dave,

It looks to me as if your scale is biased against odd numbers. In the  
numbers represented, 80 are even numbers and only 11 are odd numbers,  
a significant departure from the ~ 50:50 ratio one would expect.

Cheers,

Chris

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.
>
>    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
>
>
>
>

_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.
Christopher Majka          Email: <c.majka@ns.sympatico.ca>
Halifax, Nova Scotia, Canada   chebucto.ca/~aa051/Profile.html

"I have discovered the art of deceiving diplomats. I speak
the truth and they never believe me."   - Camillo di Cavour
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._.


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<HTML><BODY style=3D"word-wrap: break-word; -khtml-nbsp-mode: space; =
-khtml-line-break: after-white-space; ">Hi Dave,=A0<DIV><BR =
class=3D"khtml-block-placeholder"></DIV><DIV>It looks to me as if your =
scale is biased against odd numbers. In the numbers represented, 80 are =
even numbers and only 11 are odd numbers, a=A0significant departure from =
the ~ 50:50 ratio one would expect.</DIV><DIV><BR =
class=3D"khtml-block-placeholder"></DIV><DIV>Cheers,</DIV><DIV><BR =
class=3D"khtml-block-placeholder"></DIV><DIV>Chris</DIV><DIV><BR><DIV><DIV=
>On 3-Dec-06, at 5:19 PM, David &amp; Alison Webster wrote:</DIV><BR =
class=3D"Apple-interchange-newline"><BLOCKQUOTE type=3D"cite"><DIV =
style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; =
margin-left: 0px; ">Dear All,<SPAN class=3D"Apple-converted-space">=A0 =A0=
 =A0 =A0 =A0 =A0 </SPAN>Dec 3, 2006</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN =
class=3D"Apple-converted-space">=A0=A0 </SPAN>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'.</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN =
class=3D"Apple-converted-space">=A0=A0 =A0 </SPAN>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<SPAN class=3D"Apple-converted-space">=A0 =
</SPAN>but some intermediate weights were not represented.</DIV><DIV =
style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; =
margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style=3D"margin-top: =
0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN =
class=3D"Apple-converted-space">=A0=A0 </SPAN>The number of readings at =
each weight within this range were:</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">172; =
7</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">173; 0</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">174; =
6</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">175; 3</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">176; =
9</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">177; 0</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">178; =
15</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">179; 7</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">180; =
20</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">181; 0</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">182; =
15</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: =
0px; margin-left: 0px; ">183; 0</DIV><DIV style=3D"margin-top: 0px; =
margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">184; =
8</DIV><DIV style=3D"margin-top: 0px; margin-right: 0px