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Measuring a paper clip with precision

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  1. Oct 1, 2015 #1
    1. The problem statement, all variables and given/known data
    You are asked to find the weight of a paper clip as accurately as possible and given ten paper clips and a scale that has a precision of 0.1 g. (A paper clip weighs about 1 g.) Which of the following proceedures would give you the most precise measurement the weight of a paper clip?

    1. Weigh each paper clip individually, average the values and calculate the standard error.
    2. Place all ten paper clips on the scale at once, then divide the value and the precision of the scale by ten.
    Explain your reasoning.

    2. Relevant equations
    N/A

    3. The attempt at a solution
    Precision is how close the measured values are to each other. With this being said procedure two would provide the most precise measurement. Procedure one would be much more accurate because it is measuring each paper clip individually to find how close the measurement of the weight is to the actual weight (1.0g). In procedure two all ten paper clips are measured at once meaning the value of the weight divided by 10 would be the average.


    I am not sure if my reasoning is correct. Any thoughts?
     
  2. jcsd
  3. Oct 1, 2015 #2

    phinds

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    This is, I think, an ill-worded problem. It says "find the weight of a paper clip". Why measure more than one if you are just looking for the weight of one, and why even ask for the error when you know that the scale has a specified error? If in fact the problem wants the average weight, then doing all 10 at once is much better since you still only have an absolute error the same as if you measured just one.
     
  4. Oct 1, 2015 #3

    haruspex

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    First, I second phinds' objection that the question ought to be asking for how best to detemine the average weight of the ten paperclips.

    In your attempt at solution, I'm not sure which you are saying gives the better estimate of the average weight. You seem to be having a bet each way. And I see nothing there that constitutes a reason - you merely assert that one or other is better.

    Are you familiar with concepts such as independent random variables, identical distributions, variance, expected error and sample sizes?
     
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