## Statistics and Percentiles

So far in our business forecast **risk model**, we've looked at charts of the full range of Net Profit outcomes, in the form of a **frequency** bar chart. As shown below, the **Statistics **pane in theUncertain Function dialog provides a variety of statistics for the current set of simulation trials. For instance, we see that the minimum and maximum net profit values were -$66,869 and $211,052, respectively. (These same statistics could be computed in the spreadsheet using **PsiMin(F10)** and **PsiMax(F10)**, respectively.) The **Value at Risk 95%** statistic shows that we have a 5% chance of making $173,752 or more, and the **Conditional Value at Risk** **95%** statistic shows that the average of all the observed Net Profit values below the VaR 95% level is $87,454. (These same statistics could be computed in the spreadsheet using **PsiBVar(F10,0.95)** and **PsiCVar(F10,0.95)**, respectively.)

Also note that an Upper Cutoff value of 175 has been entered in the Statistics pane (above), resulting in a second red vertical line in the chart at this value. The top of the chart now indicates that 4.6% of the simulation trials produced net profit values in excess of $175,000 -- and 88.1% of the net profit values fell between $0 and $175,000.

Another view of the full range of outcomes is shown on the **Cumulative Frequency **tab, shown below. Each bar on this tab shows the frequency with which Net Profit was less than or equal to the value on the horizontal axis. The **Percentiles **pane in the Uncertain Function dialog shows the same information as the Cumulative Frequency tab, but in numeric form.

We now have a pretty good idea of the **full range of outcomes** for Net Profit. In a conventional what-if spreadsheet model, we'd now be asking "How can we increase Net Profit?" But with a risk analysis model, we can also ask and answer questions like "How can we **reduce the chance of a loss**?" and "How can we **reduce the variability** of Net Profit?" Sensitivity analysis can help us answer all these questions, as discussed on the next page.

**< Back to: Viewing the Full Range of Profit Outcomes**

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