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title: "Statistics of Monte Carlo simulation results"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574968/Statistics%20of%20Monte%20Carlo%20simulation%20results"
format: markdown
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# Analysis of Monte Carlo simulation results


The generated random values from a Monte Carlo simulation are samples from the theoretical probability distribution of the output. The more iterations n one runs, the closer one will be to the theoretical probability distribution. We will use the profit of a project as our model output in this example:


| **Continuous variable** |
| --- |
| **Parameter** | **Description** | **Definition** |
| Percentiles | P% of the generated values fall at or below x<sub>P</sub> |  |
| **Location** |  |  |
| Mode | The most frequently occurring value if the output is discrete. Otherwise it is estimated by finding the point of the steepest gradient for the empirical cumulative distribution. |  |
| Median | 50% of the generated values fall at or below x<sub>50</sub> |  |
| Mean | The average of the generated values. | > Macro (inline-media-image)

> Macro (mathinline) |
| **Spread** |  |  |
| Standard deviation | The square root of the variance | > Macro (inline-media-image)

> Macro (mathinline) |
| Variance | The average squared distance between each value and the mean | > Macro (inline-media-image)

> Macro (mathinline) |




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