Finding the Relative Uncertainty for the Standard Error of the Mean

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SUMMARY

The discussion focuses on calculating the relative uncertainty of the Standard Error of the Mean (SEM) using the formula \(\frac{\sigma_A}{A}\). Participants clarify that the relative uncertainty of SEM can be determined by dividing the SEM by the corresponding mean value. The provided data includes means, standard deviations, and SEMs for five different datasets, which are essential for performing these calculations accurately.

PREREQUISITES
  • Understanding of statistical concepts such as Mean, Standard Deviation, and Standard Error of the Mean (SEM).
  • Familiarity with the formula for relative uncertainty: \(\frac{\sigma_A}{A}\).
  • Basic knowledge of data interpretation and analysis.
  • Ability to perform calculations involving ratios and percentages.
NEXT STEPS
  • Learn how to calculate relative uncertainty for various statistical measures.
  • Explore the implications of SEM in hypothesis testing and confidence intervals.
  • Study the relationship between standard deviation and SEM in different sample sizes.
  • Investigate advanced statistical software tools for performing these calculations, such as R or Python's SciPy library.
USEFUL FOR

Statisticians, data analysts, researchers, and students who are involved in statistical analysis and interpretation of data, particularly in understanding the concepts of uncertainty and error measurement.

Athenian
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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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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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Thanks for the response. In the end, I also interpreted the statement in the same manner.
 

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