Defining privacy in the context of statistical data analysis presents several challenges. One key challenge is ensuring that the analysis doesn't reveal new, sensitive information about individuals that isn't already publicly known. For instance, learning something about an individual that they haven't disclosed publicly could be considered a privacy breach. However, determining what constitutes 'new' information and setting the boundaries for privacy can be complex. Additionally, there's the challenge of separating what is learned about an individual versus what is learned about the population. Differential privacy addresses these challenges by focusing on the indistinguishability of outcomes regardless of any single individual's data, thereby ensuring individual privacy while allowing for population-level analysis.