[scientizscht (OP)]

Hello

Is weighted average a good representation when you have values and their probabilities which do not follow a normal distribution?

If not, what is more accurate?

[Bored chemist]

It depends on the distribution.
Some distributions do not even have a mean.

[evan_au]

It depends on what you are trying to determine about the distribution, and what you want to use it for.

There are several measures of the center of a distribution: the Mean, Median and Mode, which often give different answers for a non-Normal distribution.

There are several measures for the spread of a distribution, like the standard deviation and range.

There are even measures for the symmetry of the distribution (like skew and kurtosis).

If you want to summarise a distribution, you could use a histogram.

In the end, the best solution is determined by the problem that you are trying to solve.
So what are you trying to do with the distribution?

See: https://en.wikipedia.org/wiki/Mode_(statistics)#Comparison_of_mean,_median_and_mode

[chiralSPO]

Another common approach is to take the "root mean square" or RMS. Which is the square root of the average of the squares of the values. This is useful for things like thermal velocity distributions in ideal gasses, or voltages in an AC circuit...