A certain scale has an uncertainty of 3 g and a bias of 2 g.
a. A single measurement is made on this scale. What are the bias and uncertainty in this measurement?
b. Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?
c. Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?
d. As more measurements are made, does the uncertainty get smaller, get larger, or stay the same?
e. As more measurements are made, does the bias get smaller, get larger, or stay the same?
(a) The bias is 2 g and the uncertainty is 
= 3g.
(b)The bias is 2 g and the uncertainty is 
.
(c)The bias is 2 g and the uncertainty is 
.
(d)The uncertainty gets smaller; it is proportional to 
where n is the number of measurements.
(e) The bias stays the same. The mean of the sample average is the same no matter what the sample size, so the
bias is the same as well.
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