Find mean / median point based on ID attribute and point density (hot spots)

I have a point feature class within ArcGIS Pro, with 10.000 features, data are structured like this:

ObjectID |  MemberID | Lat | Long
1             ID_1     Y1    X1
2             ID_1     Y2    X2
3             ID_1     Y3    X3
4             ID_2     Y4    X4
5             ID_2     Y5    X5
...
10.000        ID_n     Yn    Xn

Based on:

• MemberID
• Density of points (sometime I have points very far each other and I want to give a low weight to the outliers)

I would like to have as output:

• A point feature class, in which each point represents the mean/median/avg/bestRepresentation of location for each MemberID.

I already tried with the centroid, but I don’t like the result as I would also like to take into consideration the density of points (and give a low weight to the outliers)

Is there a specific tool to do this or should I built a custom one?
Once I receive suggestions I could start to write some code below.