HomeTechniques and Tips@RISK Simulation: Graphical ResultsInterpreting or Changing the Y Axis of a Histogram

7.1. Interpreting or Changing the Y Axis of a Histogram

Applies to:
@RISK for Excel 4.5–7.x
@RISK for Project 4.0 and 4.1

How do I interpret the y axis of the histogram that is created from the results of my simulation?

The histogram created from your result data can be displayed in two different formats, probability density or relative frequency. The two histograms have the same shape; it is only the scaling of the y axis that differs. The default histogram is probability density for continuous data, and relative frequency for discrete data.

In a probability density histogram, the area of each bar represents the proportion of the data (the fraction of all the iterations) in that bar. The y axis is scaled so that the total area of the histogram bars is 1. In detail, the probability density histogram is created by:

  1. Dividing the data into intervals — see Number of Bins in a Histogram.
  2. Counting the number of data points in each interval.
  3. Dividing the counts by the total number of data points.
  4. Dividing that result by the interval width as shown on the x axis, to obtain the height of the bar along the y axis.

In a probability density histogram, the larger the numbers on the x axis, the smaller the numbers on the y axis must be to keep the total area at 1.

In a relative frequency histogram, the height of each bar represents the proportion of the data (the fraction of all the iterations) in that bar. The y axis is scaled so that the total height of the histogram bars is 1 or 100%. The relative frequency histogram is created by:

  1. Dividing the data into intervals — see Number of Bins in a Histogram.
  2. Counting the number of data points in each interval.
  3. Dividing the counts by the total number of data points, to obtain the height of the bar along the y axis.

In a relative frequency histogram, the heights of the bars are their relative frequencies, and the y axis scaling is unaffected by the size of the numbers on the x axis.  Beginning with @RISK 6.2, relative frequencies are shown as percentages.

How do I select the histogram format?

In @RISK 5.x–7.x, click the histogram icon at the bottom of the Browse results window and select Relative Frequency or Probability Density.  If you prefer, you can suppress the numbers on the y-axis entirely: right-click on any of the numbers on the vertical axis and select Axis Options. Then on the Y-Axis tab, under Display, remove the check mark by Axis.

In @RISK 4.x, right-click the histogram and select Format Graph...; then select the Type tab. In the Histogram Options section, click the drop-down arrow next to the Format field and choose Density or Relative Frequency.

Last edited: 2015-07-15

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