# uniform distrubition of lab measurement question.

• Mar 15th 2012, 01:21 AM
transgalactic
uniform distrubition of lab measurement question.
student measured the length a width of a table several times and got the follwoing results.

he measured the table with a ruller for which the distance between two of its scalemarks is 1 mimilemeter.
length:
122.1, 121.9, 122.4, 122.3, 122.1

width:
23.7, 26.1, 22.3, 23.7, 25.5, 24

A)
what is the error for measuring the length? (in cm units)
B)
what is the error for measuring the width?
C)write the formula for the error of the table area?
D)what is the table area?

how i tried to solve each one:
regarding A,B:

i was told by my prof that if we measure with an instrument that have scalses in it then the error is
0.3*(distance between two of its scalemarks) which is the error in uniform distribution
so the error is 0.03

so the error in the length and width are the same and dont dependant on the mesurments themself
they both are 0.03 correct?

regarding C,D:

i have a problem in the formula of the uniform distribution because the formula says
P(x)=\frac{a+b}{2}+0.3(b-a)
where the a and b are just the point of one scale in the ruller
so the data doesnt come into account.

what i did is a ittok the smallest and bigest mesurment as a1 and b1 for the a+b/2
and 0.01 for the error

but the problem is its wrong because a and b should be the same in the error and in the a+b/2
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• Mar 17th 2012, 06:12 AM
awkward
Re: uniform distrubition of lab measurement question.
Hi Transgalactic,

For A and B, and think you are supposed to compute the standard deviations of the measurements; that is your estimate of the error.

For C and D, do you know a formula for the uncertainty of a product? I don't think the uniform distribution enters in at all.

 The formula for the uncertainty in a product goes like this:

If $p = xy$ then
$\frac{\delta p}{|p|} \approx \frac{\delta x}{|x|} + \frac{\delta y}{|y|}$

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