Can someone help me with this lab question? If, in some experiment, you make 5 m
ID: 1391363 • Letter: C
Question
Can someone help me with this lab question?
If, in some experiment, you make 5 measurements of quantity A and 5 measurements of quantity B and calculate a set of numbers C by calculating C = A + B for each pair, how would you expect the range of the values of C to compare to the range of the values of A and B? To be specific, which statement is correct?
The range of the calculated C values should be smaller than one of the ranges of either A or B.
The range of C should be between the largest of the ranges of A or B and the sum of the ranges of both A and B.
The range of C should be larger than the sum of the ranges of both A and B.
To answer this question, what does the uncertainty propagation formula predict should be the correct statement from the above three possibilities? That is,
If C = A + B can ?C be smaller than ?A or ?B?
If C = A + B and ?A and ?B were about the same size, how would ?C compare to ?A or ?B?
Would your answers change if the resulting set of ?C values were calculated using C = A
Explanation / Answer
ANSWER:
OPTION B: The range of C should be between the largest of the ranges of A or B and the sum of the ranges of both A and B.
It is because
(delta C)^2 = (delta A)^2 + (delta B)^2
Thus, deltaC is greater than both deltaA and deltaB, but less than their sum.