Re: Uncertainty Question

[Leigh Palmer <palmer@SFU.CA>]

> I admit it, as part of my required curriculum I have to teach more about
> uncetainties than I am confident about. The rules are inconsistent from
> text to text and common sense does not always prevail. Is there a simple
> guide book?
>
> Here is my current question:
> Measuring the density of a 3x5 card as an exercise in sig.fig.s and
> uncertainty. Some groups used a micrometer to measure the thickness,
> others made a stack of 50 and measured the group with a cm ruler. This
> group measured the stack as 1.23 cm =/- .03 cm. We divide by 50 for the
> stack. How do YOU report the uncertainty?

That depends upon what you are calling the quantity you will report.

If you report the average thickness of a card in that stack then the
straightforward result, 0.246 mm +/- 0.006 mm is correct.

If you have collateral knowledge that all of the cards in the stack
have the same thickness to within a percent or so then you would
give that same answer for the thickness of any card in the stack.

If you know that the cards are not all the same thickness (they may
have been previously handled by other students in groups that either
spilled food or drink on them, or they may have been kept clean, or
they may be wrinkled) and have been shuffled, then you cannot report
the thickness of a single card at all. You must measure each of the
cards and report on the distribution of thicknesses instead.

I have a criticism relevant to this otherwise good experiment. It
shouldn't be changed, but the students should be asked to criticize
it, too. I am unwilling to believe that a stack of 3x5 cards can be
measured to this degree of accuracy without a better specification
of the system. Surely the stack is more compressible than this. The
result will depend upon the way the stack is loaded during the
measurement. Surely if the cards are counted by students they will
have thickened edges to some degree, and the thickness in the center
of the stack will be different from the thickness at its edges.
These factors are, I expect, very important if you are going to
compare the results of two measurement techniques. I can't imagine
that the micrometer measurement would give anything but a smaller
thickness result than one would get from stacked cards. I think that
critical treatment of the measurement is an important part of
learning to do the science. In this case there are assailable points,
and the opportunity to exercise critical skills should be seized
upon.

(I also feel that reporting these results in millimeters rather than
centimeters would be more appropriate, but that's just my own taste.)

Leigh