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**Sum of Percentiles Differs from Percentile of the Sum**

**Applies to:** @RISK, all releases

In my model, I have a set of inputs. I strike a sum, and that is my output. But I also compute the 95th percentiles of the inputs and the 95th percentile of the output using RiskPercentile( ) or RiskPtoX( ). Why does a percentile of the output not equal the sum of that percentile of the inputs?

This is normal behavior. Unless your inputs are correlated with a coefficient of 1, they won't all be at a given percentile in the same iteration. In most iterations, some inputs will be above any particular percentile and some will be below. When you add them all up, the highs and lows tend to balance out, so the 95th percentile of the sum will be closer to the mean than the sum of the 95th percentiles of the inputs.

It's not just percentiles — any statistic will have a similar issue. This is a statistical feature of combining probability distributions, and not any kind of problem in @RISK or in your model.

For a related issue, see Static Value of Output Differs from Simulated Mean.

**Additional keywords:** Maximum of sum doesn't equal sum of maximums; Minimum of sum doesn't equal sum of minimums

Last edited: 2015-07-22

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