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 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?

Question
Measurement
asked 2021-02-04
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?

Answers (1)

2021-02-05
Step 1
"Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved."
a)
If a single measurement is made on this scale, then the bias and the uncertainty remains the same. That is, the bias is 2g and the uncertainty is 3g.
Step 2
b)
If four independent measurements are made on this scale, then the uncertainty in the measurement is normally distributed and its value becomes half but the bias remains the same.
Step 3
c)
If four hundred independent measurements are to be made, then the uncertainty becomes,
\(\sqrt{n}=\sqrt{400}=20\)
Thus, the four hundred independent measurements were to be made then the uncertainty becomes 20 times smaller but the bias remains the constant.
0

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