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<div class="moz-text-html" lang="x-unicode"> <big><font size="2"><big><big><font
size="2"><big><big><font size="2"><big><big><font
size="2"><big>I often receive questions
about the sig. fig. in exp 16 when it
comes<br>
to averaging the f.p. determinations to
get the average f.p. which you<br>
report on your data sheet and in the
on-line pre-lab and data-entry post-lab.<br>
<br>
</big></font></big></big></font></big></big></font></big>
In class we discussed how you can average several numbers
and gain sig.<br>
fig. </big></font></big><big><font size="2"><big><big><font
size="2"><big>That is correct. That's why we take
lots of measurements and average<br>
them. However, in practice when dealing with
experimental data including<br>
an additional sig. fig. in an average or from a
graph really can't safely be<br>
done with only 2 or 3 numbers. <br>
</big></font></big> <br>
Think about exp 1 in which you were plotting your data. </big></font></big><big><font
size="2"><big><big><font size="2"><big>The purpose of<br>
a best-fit line is to average out the random error
in your data. If you had<br>
only 2 pts the line would go through both points and
wouldn't have show<br>
any effect of random errors. Adding one more point
wouldn't make it much<br>
better. Having at least 4 data points would make it
more plausible to gain a<br>
sig. fig. (both when averaging and from a graph).
Even this may not be safe<br>
as it actually depends on the magnitude of the
numbers. However, I stated<br>
for the purposes of this class if you have 4 or more
data points you can<br>
gain a s.f.<br>
</big></font></big></big></font></big><br>
<big><font size="2"><big><big><font size="2"><big><big><font
size="2"><big><big><font size="2"><big>I
discussed this back in week 1 when
discussing s.f. and again recently in<br>
an e-mail about exp 12.<br>
</big></font></big></big></font></big></big></font></big> <br>
When you add up your determinations for the f.p. for each
trial adding only<br>
three values isn't enough to give confidence in reporting
an extra s.f. If you<br>
did five determinations and averaged those I would say you
could maybe<br>
report 1 extra s.f., but that depends on the actual data.
This will certainly<br>
</big></font></big><big><font size="2"><big><big><font
size="2"><big>not be the case for the pre-lab since it
gives the f.p. of the cyclohexane and<br>
in each trial (it's already "averaged" some unseen
determinations). </big></font></big><br>
<br>
Dr. Zellmer</big></font></big> </div>
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