Math
Standard deviation
Calculate population mean, variance and standard deviation for five values.
Calculators / Math / Triangular distribution moments
Triangular distribution moments calculator
Find the mean and spread of a triangular probability model from its bounds and mode.
On this page
Expected value4.67
Variance4.22
Standard deviation2.05
Calculator controls
How to calculate
Find the mean and spread of a triangular probability model from its bounds and mode.
Expected value =
(a+m+b)/3Variance =
((b-a)^2+(m-a)^2-(b-a)*(m-a))/18Standard deviation =
sqrt(((b-a)^2+(m-a)^2-(b-a)*(m-a))/18)Worked example
- Minimum value: 0
- Most likely value: 4
- Maximum value: 10
- Expected value: 4.67
- Variance: 4.22
- Standard deviation: 2.05
Assumptions and limits
Minimum must be below maximum, with the mode inside the bounds. A triangular assumption is a model, not evidence that extreme values cannot occur.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the mean and spread of a triangular probability model from its bounds and mode. Use a common measurement unit. Variance has squared units; standard deviation and the expected value retain the original unit.
When this tool is useful
Use a common measurement unit. Variance has squared units; standard deviation and the expected value retain the original unit.
Understanding your inputs
| Input | Example |
|---|---|
Minimum value a | 0 |
Most likely value m | 4 |
Maximum value b | 10 |
Frequently asked questions
What does this model leave out?
Minimum must be below maximum, with the mode inside the bounds. A triangular assumption is a model, not evidence that extreme values cannot occur.
How do I reproduce the example?
Enter the displayed example values in their labelled units. Apply the formula before rounding; change one input at a time to compare scenarios.