Anomalous activity that significantly deviates from normal patterns could indicate a security breach. Examples are provided of outliers that may warrant further investigation, such as a single IP address sending over 100,000 tweets in one day, an employee uploading 4.5 GB of files to an unsecured cloud service, or a manufacturing employee uploading 48.7 GB of data to an external sharing site in a single day. The document recommends monitoring for anomalous outliers to detect potential breaches early before they can seriously impact the business.