Human Activity Recognition (HAR) using sensor data is vital for healthcare but raises privacy concerns with traditional centralized machine learning (CML) approaches. This thesis compares CML with Federated Learning (FL), which keeps data on local devices, using the UCI HAR dataset and LSTM models. Three FL aggregation methods: FedAvg, FedProx, and Krum, are evaluated under both IID and non-IID data, with and without Local Differential Privacy (LDP) and data poisoning attacks. Results show FL outperforms CML in accuracy and privacy, with FedAvg achieving the best results in non-IID settings and Krum offering strong robustness to attacks. However, stronger privacy via LDP reduces accuracy, highlighting a privacy-utility trade-off. Overall, FL, especially with FedAvg, is effective for privacy-preserving HAR in healthcare.