This isn't a specific problem. It's more of something that I have encountered before and I have been unable to find an answer to by looking online or through notes. Hopefully this thread might serve others with similar problems in the future.
Say for example, you want to measure the speed of sound experimentally, and you get four values from four attempts:
340 ± 1 m/s
345 ± 5 m/s
341 ± 2 m/s
335 ± 20 m/s
It seems sensible to average the data to get a value which will hopefully be a good estimate. That is not too difficult, but how would one deal with uncertainty in this case?
I'm not really sure.
The Attempt at a Solution
The mean of these values gives a speed of sound of 340 m/s correct to one decimal place.
I have been told that the error of the average is not the average of the error, so that would eliminate using ± 7 m/s as the uncertainty. The standard deviation can be used to give an uncertainty of ± 4 m/s but that ignores the uncertainty in each of the measured quantities.
Another way of obtaining uncertainty is to subtract the smallest obtained value from the largest and divide it by the number of samples, giving (345-335)/4 = ± 2.5 m/s but this also ignores the measurement uncertainty.
What is the appropriate course of action in this case? Thanks in advance.