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February 22nd, 2019, 12:46 PM   #1
Sin
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Mean of means - standard deviation of mean values

Sorry if this has been asked numerous times and sorry if I describe it from an engineers point of view.
Let us say I have N measurements and I calculate the mean value and the standard deviation. Okay.
Now let us have M times N measurements. I could calculate now the mean value of the whole number of values and calculate the standard deviation.
I additionally could calculate the mean value of the standard deviations of the M measurement series but I could - and this is my question about - calculate the standard deviation of the mean value.
My question: How does this value help me? What does this value describe?
For me this value seems to correct the measurement in a very strong way because a factor of 1/sqrt(M) is significant. How do I have to understand the standard deviation of the means?
Doesn't this mean that I can simply subdivide a dataset of X numbers to N*M numbers and then find a pretty precise mean value and in this sense a pretty reliable measurement result? Can I profit from this trick?
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February 23rd, 2019, 11:01 AM   #2
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https://en.wikipedia.org/wiki/Standard_error
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