Interpreting Histogram Y-Axis in @RISK

Applies to:

• @RISK for Excel 4.5 and up

• @RISK for Project 4.0 and 4.1

Overview

@RISK can display simulation results as a histogram in two formats: Probability Density or Relative Frequency. The choice affects only the scaling of the Y-axis; the histogram’s shape remains unchanged.

• Default: Probability Density for continuous data, Relative Frequency for discrete data.

• Tip: Relative Frequency is often easier to interpret, especially for presentations. You can also suppress the Y-axis if desired.

Interpreting Relative Frequency

• The Y-axis shows the percentage of iterations in each bar.

• Example: If a bar reaches 2%, this means 2% of all simulation iterations fall within that interval.

• The heights of all bars sum to 100% (or 1 if decimals are used in older versions).

Note: Before @RISK 6.2, Relative Frequency was displayed as decimals (0.02 instead of 2%).

Interpreting Probability Density

• The height of a bar alone is not meaningful. The area of the bar determines the percentage of iterations in that interval.

• Example: For a bar from $74,000 to $76,000 with a height of 4.9×10⁻⁵:
  [
  \text{Area} = \text{width} \times \text{height} = 2,000 \times 4.9\times10^{-5} \approx 0.098 = 9.8%
  ]
  This means 9.8% of iterations fell between $74,000 and $76,000.

• Total area of all bars = 1 (or 100%).

Theoretical probability curves:

• Curves are always probability density.

• The height alone is not meaningful; the area under the curve represents the proportion of data in that region.

• Example: If the area under a Normal(80,000, 4,800) curve left of $72,104 is 5%, theory predicts 5% of values fall below $72,104.

How @RISK Creates Probability Density Y-Axis

1. Divide data into intervals (bins).

2. Count the number of data points in each interval.

3. Divide by the total number of data points.

4. Divide by the interval width to get the bar height.

Note: For probability density, larger X-axis ranges require smaller Y-axis values to keep the total area at 1.

Changing the Y-Axis Format

• @RISK 5.x–7.x:

  • Click the histogram icon at the bottom of the Browse Results window.

  • Choose Relative Frequency or Probability Density.

  • To hide Y-axis numbers: Right-click a number → Axis Options → Y-Axis tab → uncheck Axis.

• @RISK 4.x:

  • Right-click histogram → Format Graph → Type tab → Histogram Options → Format → Density or Relative Frequency.

Tip: Change the default in Utilities » Application Settings » Simulation Graph Defaults → Preferred Distribution Format.

Summary Table

Y-Axis Format	Meaning
Relative Frequency	% of iterations in each bar
Probability Density	Area of bar (height × width) = % of iterations; height alone ≠ %