This is a very common question in all kinds of scientific measurements.Fortunately, the answer is straightforward:
Example: |
The standard deviation measures the width of the distribution
of the individual measurements Xi. (The square of the
standard deviation is also known as the variance).
Example: |
which we simply obtain from the standard deviation by division
by the square root of n. This standard deviation of the
mean is then equal to the error, dX
which we can quote for our measurement.
Example: |
Thus the combined result of performing n independent
measurement of the same physical quantity is the mean plus/minus
the standard deviation of the mean.
Example: Note that we have rounded the quoted error to the first significant digit and then also rounded the quoted mean value to the same accuracy. |