Finding the Relative Uncertainty for the Standard Error of the Mean

In summary, the conversation is discussing how to find the relative uncertainty of standard error of the mean (SEM) using the equation ##\frac{\sigma_A}{A}##. The question is asking for ideas on how to calculate this, and after further discussion, it is determined that the relative uncertainty of the mean is equal to SEM divided by the mean.
  • #1
Athenian
143
33
Homework Statement
Get the relative uncertainty for the standard error of the mean. Afterward, multiply the value by the logarithm of the mean to obtain the uncertainty in the graph.
Relevant Equations
N/A
While I will not be showing the graph here, I am trying to dissect what the question even means.

While I do understand that relative uncertainty can be found via the equation ##\frac{\sigma_A}{A}##, I do not understand how I can find the "relative uncertainty of SEM". Does anybody here have any ideas? Please refer to the table below for the data.

MEANSTANDARD DEVIATIONSTANDARD ERROR OF THE MEAN (SEM)
156.0083​
3.258683​
0.940701​
131.1333​
1.830218​
0.528338​
74.38333​
2.361368​
0.681668​
48.175​
2.965905​
0.856183​
31.275​
2.205005​
0.63653​
14.45833​
2.589299​
0.747466​

Thank you for reading through this short question!
 
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  • #2
I think they want what I would have called the relative uncertainty of the mean, i.e. SEM divided by the mean.
 
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  • #3
Thanks for the response. In the end, I also interpreted the statement in the same manner.
 

FAQ: Finding the Relative Uncertainty for the Standard Error of the Mean

What is the standard error of the mean?

The standard error of the mean is a measure of the variability or uncertainty in the sample mean. It tells us how much the sample mean is likely to differ from the true population mean.

Why is it important to find the relative uncertainty for the standard error of the mean?

Finding the relative uncertainty for the standard error of the mean allows us to determine the precision of our sample mean estimate. It helps us understand the range of values within which the true population mean is likely to fall.

How is the relative uncertainty for the standard error of the mean calculated?

The relative uncertainty for the standard error of the mean is calculated by dividing the standard error of the mean by the sample mean and multiplying by 100. This gives us a percentage that represents the uncertainty in our sample mean estimate.

What factors can affect the relative uncertainty for the standard error of the mean?

The relative uncertainty for the standard error of the mean can be affected by the sample size, the variability of the data, and the confidence level chosen for the calculation. A larger sample size and lower variability will result in a smaller relative uncertainty.

How can the relative uncertainty for the standard error of the mean be interpreted?

The relative uncertainty for the standard error of the mean can be interpreted as the amount of error or variability in our sample mean estimate. A smaller relative uncertainty indicates a more precise estimate, while a larger relative uncertainty indicates a less precise estimate.

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