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So I was calculating the sample standard deviation values for 5 trials and I noticed that the values were really close to the absolute uncertainty of the mean found using the formula: (max - min)/2

Are they the same thing? If I want to plot error bars on a graph, could I use the standard deviation values instead of the absolute uncertainty values since they are basically the same (according to me)?

Justin
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  • I've never seen (max-min)/2 called the "absolute uncertainty of the mean". That formula doesn't compute anything about the mean at all, nor is it any kind of measure of uncertainty. It's simply the range divided by 2. – Nuclear Hoagie Feb 18 '21 at 18:25
  • @NuclearHoagie - Could you help me understand the difference between “uncertainty in a measurement” and “uncertainty in the mean” on [page 4 of this document](https://www.physics.upenn.edu/sites/default/files/Managing%20Errors%20and%20Uncertainty.pdf)? – Justin Feb 18 '21 at 18:31
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    Range/2 makes more sense as an uncertainty measure in the context of repeated measurement on the same sample (not sure if that's the case here), like if you measure someone's height 5 times. This give a sense of how precise/uncertain your measurement tool/technique is. The uncertainty in the mean, on the other hand, usually goes down as you take more measurements, since positive and negative errors will average out and more data gives you less uncertainty. – Nuclear Hoagie Feb 18 '21 at 18:44

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No, it is just a coincidence that they happened to be close in the cases you looked at. If the data are normally distributed, there is an approximate formula for expected value of minimum and maximum in random samples from normal distribution. That only gives you a formula for the expected value, the actual value in a sample will vary from one set of data to the next.

Some tables report the population mean plus or minus 2 standard deviations as a range of values that includes approximately 95% of the data. So, the difference between that upper limit and lower limit divided by 2 will be approximately equal to twice the standard deviation.

John L
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  • So in my case, can I plot the standard deviation values as error bars, or is plotting absolute uncertainties as error bars better (or correct)? – Justin Feb 18 '21 at 18:29
  • If you are plotting boxplots, there are different conventions. I don't know enough about what you are trying to plot to answer. – John L Feb 18 '21 at 18:49
  • I've taken 5 trials and I've come up with a line graph with 5 points each with an error bar. But I don't know if I should use the absolute uncertainty values or the standard deviation values... – Justin Feb 18 '21 at 18:52