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Unformatted text preview: k of drawing a straight line all the more
If we simply draw a line from the first point to the last point, then we have drawn
a two-point curve and there was no reason to take more experimental measurements than
just these two points. Instead, we want a line that best fits as much of the experimental
data as possible. To do so, place a straight edge amongst the experimental data. If the
curve must intercept at zero (or some other point), fix this side of the straight edge.
Typically, however, there are no requirements for the intercept. Now move the straight
edge such that when you draw the line, it looks as if the error above the line is about
equal to the error below the line.
At this point, you’re probably wondering what I mean. Well, if we assume that
the error is uniformly distributed amongst all of the data. That means that I should have
as much error that is too high as error that is too low. Recall that we assumed the “x”
values are exact, and the only error is in the “y” values. So, if we were to measure the
distance from each point to the line drawn for those points above the line, this sum should
be equal to the sum of the distances from the points below the line to the line. Now, we
needn’t be so exact as to actually take these measurements and do the summations, but
try to draw a line so that if we were to do this, the two errors would be as close as
In some graphs, this is easier to do than in others. Typically (but not always),
we’ll have about as many points above the line as below (in our example, it is two above
and three below). However, really we are drawing a line so the points look as randomly
distributed about that line as possible. There are mathematically exact ways to determine
the line that best fits data, but we shall not go into this here. If you would like to learn
how to do this (it is called “Linear Regression”), please consult a statistics textbook or
stop by my office and ask. I’ll be happy to teach this technique to any who would like to
learn it on an ind ividual by-request basis.
Most of the time, we cannot discard data. In our present example, the points are
so greatly spread out that I cannot assume that any data can be discarded. Typically, the
only time it is acceptable to discard one experimental point is if it is clearly far off from
the line that could be drawn without it. That is, if all of the points lie very very close to a
line and one point is extremely far off, then most likely that one point is an exception and
can be discarded. However, typically too few points are taken to be able to do this. If
you feel that you have a point that should be discarded for any reason, talk with your
professor and ask his/her opinion before discarding.
Reading a Point:
So now we want to find a point. We want to use our results to estimate the
boiling point of methane (16 g/mol). Now we draw a line from the “x” axis at 16 g/mol) Dakota State University page 216 of 232 Plotting...
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