Human activity recognition (HAR) algorithms today are designed and evaluated on data collected in controlled settings, providing limited insights into their performance in real-world situations with noisy and missing sensor data and natural human activities. We present a real-world HAR open dataset compiled from a wristband equipped with a triaxial accelerometer. During data collection, participants had autonomy in their daily life activities, and the process remained unobserved and uncontrolled. A general convolutional neural network model was trained on this dataset, achieving a mean balanced accuracy (MBA) of 80%. Personalizing the general model through transfer learning can yield comparable and even superior results using fewer data, with the MBA improving to 85%. To emphasize the issue of insufficient real-world training data, we conducted training of the model using the public MHEALTH dataset, resulting in 100% MBA. However, upon evaluating the MHEALTH-trained model on our real-world dataset, the MBA drops to 62%. After personalizing the model with real-world data, an improvement of 17% in the MBA is achieved. This paper showcases the potential of transfer learning to make HAR models trained in different contexts (lab vs. real-world) and on different participants perform well for new individuals with limited real-world labeled data available.