# Likelihood of an observation for a small sample size

I am trying to understand how much an observation is compatible with other data, given that the sample size of this other data is very small ($$n=5$$).

In practice, I have several measurements: $$x_{1}, x_{2}, \dots, x_{n}$$. Given that $$n$$ is small the pure statisical error on the model is large. Now I have another observation $$x_{0}$$, and I would like to know how compatible this observation is with the rest of the data.

If I'm not mistaken (and I may since my background in statistics is bad), what I want is the likelihood of $$x_{0}$$ given $$x_{1}, x_{2}, \dots, x_{n}$$. For the sake of simplicity, I am assuming a gaussian distribution. But how to properly propagate the errors?