## SIMULATION OUTPUTS

In **Quantitative Risk Analysis**, many of the outputs are talked about in terms of things like “P50” or “P80” or “P95 – P5”, as well as statistical terms like Mean, Median, Mode, Standard Deviation, Variance, Sigma…

It is important to understand the differences between mean, median and mode:

**Mean** represents the **average value** of the distribution, i.e. all the results added up and divided by the number of iterations.

**Median** represents the value that is in the **middle** of the distribution i.e. half of the iterations will have produced a number higher than the median, and half will have produced a lower number.

**Mode **or** Most Likely** represents the value in the distribution that occurs **most frequently**.

The graph below summarises these:

## IT’S ALL A CONFIDENCE TRICK

**P80** (for example) is shorthand for the 80th percentile. In the context of the output from a QRA, it means that 80% of the results coming out of the simulation are lower than that P80 value.

Or to put it another way, based on the simulation, we can be 80% confident that the final outcome will be lower than the P80.

## WHAT DOES IT ALL MEAN?

One needs to be very careful when using P80 results, particularly for Cost QRAs. This is because they represent points on a statistical distribution and **statistical distributions cannot be added** (if they could we wouldn’t need to do Monte Carlo simulations!). The **one exception** to adding statistics together is that you **can add Mean values together** (becuase they are averages! and already made up of values being added).

So, when you have a table of risk outputs presented to you by an eager risk analyst, do not be surprised when you do what almost everybody does – add up all the values in a column to check that they add up, and find that they don’t. (P.S. This is how the insurance industry makes a profit – by adding lots of risks together and using the premiums from all those customers who don’t claim to cover the claims of those customers who do)