# How to test which data match model at best

### Description

I have 1D data with $N$ normally distributed clusters. I have to find a cluster, which is the worst (differs at most from the normal distribution).

### My approach

I calculate $sq = \frac{(f(x) - y)^2}{\#y}$, where $f(x)$ is value of normal PDF with mean equal to the center of the cluster and sigma equal to cluster's "radius", $\#y$ is the total number of observations. Cluster with highest value of $sq$ is considered to be the worst one.

### Question

Problem is that number of points per cluster differs a lot (one cluster could have 3000 points and other 300). And imho I think that if I had small errors and many points, I would end up with larger $sq$, then if I had bigger errors and small amount of points.

Can you point me the right way?