---
title: "Difficulty of interpreting the vertical scale"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575468/Difficulty%20of%20interpreting%20the%20vertical%20scale"
format: markdown
---
The most common ***mistake***** **in interpreting a histogram plot of generated values from a Monte Carlo simulation is to read off the *y*-scale value as the probability of the *x*-value occurring. This is correct <u>only</u> if the output variable is discrete and there is only one allowed value in each of the histogram classes. However, in most situations, the output is continuous, and so the probability of any individual value occurring is zero (technically, it is [infinitely small](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26574888/)).

  


Some software tools scale the vertical axis of its forecast windows as relative frequency plots only.

  


### Relative frequency histogram plots

![image](media://42458361-b911-4577-875c-49febde8ce57)

  


Figure 1: Histogram "relative frequency' plot. In these plots, the vertical scale is calculated as the fraction of the generated values that fall into each histogram bar's range. Thus, the sum of the bar heights equals unity (1). Relative frequency is strictly appropriate for discrete variables (right), where the histogram heights now sum to unity because for continuous variables (left), the area under the curve does not sums to unity.

  


  


Another way to scale the vertical axes of a histogram plot of generated values from a Monte Carlo simulation, is as 'density plots' (note that the vertical axes is *different* for the two left graphs that shows a continuous output). Although this is the *correct* way to plot continuous forecast data, some software packages do not provide this option.

### Density histogram plots

![image](media://c08d6b86-fe06-4ec4-b404-21c82398ff59)

Figure 2: Histogram "density' plot. In these plots, the vertical scale is calculated so that the sum of the histogram bar areas equals unity. This is only appropriate for continuous outputs (left). Some software packages, like Crystal Ball, call this a frequency plot while using "probability" for the label in the vertical axis. However, Crystal Ball does not provide the option to scale the vertical axis, resulting in a plot where the probability values make no intuitive sense. For example, in the right plot, the probabilities appear to exceed unity. To calculate the probability of certain output value suing the density graph, we need to know the width of the histogram bar.

  


  


  


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