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I have the following values from several measurements (they contain both systematics and statistical errors):

$25.885\pm 1.851, 26.139\pm 0.979, 27.404\pm 2.049, 30.230\pm 6.729$

If I do a simple weighted average mean I get this: $26.350\pm 0.792$, but I am not totally sure if this is right. If I had just statistical errors (and trusted them well), it would be the right thing to do, but given that I have systematics, too, it seems that the error ends up being a bit too small (for example I don't account for the scatter in the values of the means). Is there a better way to estimate the mean and the error on the mean for this data? Thank you!

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Where do the measurement errors come from? I would suggest you discard the last measurement which has a relatively much higher error than the others. Calculate the mean of measurement values and errors based on the first three experiments.

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  • $\begingroup$ The errors are partly statistical, partly systematic (added in quadrature). So if I remove the last point, can I just do a weighted average? Why would I remove the last point? It is still consistent with the other 3 and a proper analysis of the errors should give it a small weight. I am not sure tho what is the best analysis to do. $\endgroup$
    – JohnDoe122
    Apr 6, 2020 at 4:55

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