If I remember correctly, the result of your calculation is the standard deviation of the mean of your sample values. The probability distribution of the mean is normal, with that reduced standard deviation. So if you want confidence limits on the mean value, base them on that.

Dear Shahid Uz Zaman,

The formula that you use "Standard deviation/√number of data" is valid for a series of replicate measurements sampled from a stable statistical population. It is assumed that all the data are characterized by the same parameters of their statistical distribution. If you combine data obtained from different sources, this basic assumption is not met, and to combine these data you need to take their associated uncertainties into account. Both the mean value and the uncertainty of the combined results are then evaluated using statistical weights commonly taken to be squared standard uncertainties of the individual results. Other complications such as discrepancy (bias) and correlation among the results should also be taken into consideration.

In the absence of a standardized approach, paying attention to all these details is essential. A useful discussion of the problem can be found in a review paper:

W. Hasselbarth and W. Bremser. Combination of results from several meaurements - An overlasting problem. In: Combining and Reporting Analytical Results. Ed. by A. Fajgelj, at al. RSC Publishing, 2007. p. 34.

Dear Rouvim Kadis,

Thanks for your answer. The data I used for the uncertainty calculation was taken from the same source. In this case, shouldn't the formula serve the purpose?

Dear Shahid Uz Zaman,

Please keep in mind that the formula we discuss is a kind of idealization. It will serve the purpose if the following simplifications are accepted:

1) Uncertainty evaluation is restricted to random variability (which means that standard uncertainty is replaced by standard deviation). In other words, no type B standard uncertainties are taken into account.

2) Standard uncertainties of individual results to be combined are the same.

3) We have a set of independent replicate measurements so that correlation effects can be neglected. (Neglecting correlation results in underestimation of the uncertainty of the mean value.)

Whether these simplifying ussumptions are fulfilled is up to you.

Regards,

Rouvim Kadis