How can a set of points plot a graph and cut off the noise (outliers)?

Question

Mathematics

There is a data set of the form the result of measurements for such and such a day. These measurements are not always accurate and there are occasional spikes.
Question: how to build a graph of these measurements and evaluate trends, but at the same time cut off bursts?
And another question: are there any estimates for the accuracy of interpolation and extrapolation, as well as filtering out noise, depending on the amount of input data?
I'm pretty sure it's something similar to Excel (or LibreOffice), but in general, the choice of tool is unimportant. But it would be better if it was something simpler.
PS The solution is required for a person who is not strong in programming at all. And it is unlikely to master R, for example. So the simpler the better.

Answer 1

It is convenient to use R for processing statistics.
There are several articles on it on Habré.
If you just plot a graph, then gnuplot can handle it.

Answer 2

a 2D graph is built: time interval (between neighboring events) / value, then an area of ​​\u200b\u200bclusters
is visible on it - such as a galaxy and separately scattered "stars" ... We find the center of mass and, according to tolerance, we filter it out.

Answer 3

If the plot of the measured parameter is more or less smooth, then the simplest thing is to replace it with a moving average or a moving median with a window of several elements.