A Estimate of Errors

For a series of equivalent and independent observations y (i=l...AT), the mean or average value is  

If N tests have been made, one would not, of course, just pick out one measurement and regard this as the best estimate of the quantity being measured. Rather, one would report the mean value. If a series of such mean values were generated, these would also have a certain standard deviation, which would be smaller than the standard deviation of the individual results. The standard deviation in the mean values can be found directly from the standard deviation of the individual results  

We refer to a basic book on statistics for derivation of these results (e.g. Kreyszig, 1970). 

If one wishes to estimate the variance (or standard deviation) in a result calculated from a number of data f x,y,z...), each of which have certain standard deviations themselves, we can use Gauss formula for error propagation  

Let us apply this to the issue of cyclone or swirl tube efficiency. We stated in the main text that including the overhead fraction when calculating the efficiency would result in lower errors. 

---