Gnuplot error weighted mean

Question

I have a set of data with y error bars. I can find the mean of the data without error bars using the following:

f(x)=mean_y
fit f(x) "data" via mean_y

However, I want do find a weighted mean, taking into account the error bars. Is something like this possible in gnuplot or do I have to code it?

Thanks in advance.

Answer 1

You can use the using parameter to specify a column for the errors. With three using specifiers, the third one is interpreted as standard deviation s and is used to compute a weight 1/s**2 for the corresponding value:

f(x) = mean_y
fit f(x) "data" using 1:2:3 via mean_y

That assumes, that your data file has three columns, x, z and stdev. If you only have two columns, z and stdev, you must use

fit f(x) "data" using 0:1:2 via mean_y