## Risk Analyst

### Why the mode?

Simulation deals with distributions, which are long arrays of values that may take various shapes. In the Quick Help window you can see pictures of all distribution functions supported by Risk Analyst. To get the most from this variety of distributions, it is important to have a good understanding of the common measures that describe distributions: central tendency and dispersion, or, more simply, mean, mode and standard deviation.

The following picture shows the result for several measures computed on the same variable. The user is referred to any book of basic statistics for a technical explanation. Readers can also find information in the chapters Quality Analyst and Descriptive Analyst of the MM4XL User Manual.  We would like to just briefly discuss the measure of central tendency known as mode. The modal value, or mode, is the figure repeated most often during the simulation trials of one individual variable. In the picture above we see that out of 100 trials, the figure 367 was returned 14 times, and has the highest frequency among all bars. 367 is the modal value of the distribution shown in the picture. In other words, it is the value with highest probability of being sampled.

The mode is an important measure in simulation because it is often used to replace random numbers on the computer screen. Risk Analyst, as well as other popular software for risk analysis, can show the result of its functions either as random number or as mode.

For instance, the function mmBINOMIAL(5, 0.5) returns a random value ranging from zero to 5 and its modal value is 2. Every time the sheet is recalculated a new random value between 0 and 5 is shown in the cell. When Risk Analyst is set to show modal values, however, the function returns always the modal value 2, even when the sheet is recalculated, because the mode of the Binomial distribution identified with the arguments Trials equal to 5 and Successes equal to 50% is always equal to 2, verify this statement using the Risk Analyst Wizard.

On one hand, it can be an advantage to deal with a model that does not change its figures every time a change is made in a cell. On the other hand, modellers are required to develop a certain level of sensitivity on the subject of distribution functions and their shape in order to have tight control on their work. Understanding how the mode works is a good first step.

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