Aggregation need not directly threaten privacy. An aggregate (such as sum, median, or count) often depends on so many data items that the sensitivity of any single contributing item is hidden. Government statistics show this well: Census data, labor statistics, and school results show trends and patterns for groups (such as a neighborhood or school district) but do not violate the privacy of any single person.
Inference and aggregation attacks work better nearer the ends of the distribution. If there are very few or very many points in a database subset, a small number of equations may disclose private data. The mean of one data value is that value exactly. With three data values, the means of each pair yield three equations in three unknowns, which you know can be solved easily with linear algebra. A similar approach works for very large subsets of the entire database. Mid-sized subsets preserve privacy quite well. So privacy is maintained with the rule of n items, over k percent,
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