Federated k-means and k-median (FKM) clustering are powerful unsupervised learning techniques that adapt established algorithms for privacy-preserving, distributed scenarios. These methods are especially valuable in domains like life sciences and clinical research, where data is highly sensitive, very valuable, and costly to obtain. Our novel algorithms enable effective clustering without sharing raw data, thus ensuring high privacy standards while leveraging distributed computational resources. To robustly validate our approach, we perform extensive experiments on large datasets, thereby obtaining statistically sound evidence of our method's efficacy compared to state-of-the-art techniques. This rigorous evaluation also includes efficiency and scalability studies of our framework under realistic conditions. Overall, this project will not only advances the field of federated unsupervised machine learning algorithms, but also to empower and safeguard sensitive data analysis tasks in practice.