Scientific Investigations Report 2007–5185

**U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5185**

**Figure 3.** Percentiles from two hypothetical normal distributions, A and B, as well as two distributions resulting from the addition of A and B. Distribution C is the random sum, in which members of distributions A and B were chosen randomly and added together. Distribution D is the ranked sum, in which the members of distributions A and B first were ranked, then paired according to their ranks and summed. The ranked sum results in the same mean but a wider distribution, resulting in larger 95^{th} percentiles. The 95^{th} percentile of D is equal to the sum of the 95^{th} percentiles of A and B.