When all possible outcomes of an experiment are equally likely to occur, this is a uniform distribution.

The formula for uniform distribution calculates the probability of a desired event occurring within an existing interval.

We can calculate the variance of uniform distribution to demonstrate the spread or degree of dispersion of the values of the probability distribution.

The variance of the distribution is σ2 = (b – a)^2 / 12. In this formula b is the maximum value of the interval, a is the minimum.

For example, some plane spotters are tracking flights at a busy airport, they know flights takes off every 45 – 60 minutes, but they also want to calculate the spread of the take-offs. In this example the maximum value of the interval is 60, the minimum is 45.

## Steps To Calculate The Variance Of A Uniform Distribution

The steps below will take you through the process using sample data, using the above scenario.

1. Open the spreadsheet **How To Calculate The Variance Of Uniform Distribution In ****Excel.**

2. The equation to calculate the variance of uniform distribution is =**(b – a)^2 / 12**

**b =**maximum values of the interval**a =**maximum values of the interval

3. Identify the maximum values of the interval - 60 minutes in our example.

4. Identify the minimum values of the interval - 45 minutes in our example.

5. In **C5** enter **=(C3-C2)^2/12, **press Enter.

6. Excel displays the variance**.**

** **

## Quick Reference

- Open a spreadsheet
- Identify the maximum values of the interval -
**b** - Identify the minimum values of the interval -
**a** - The equation to calculate the variance of uniform distribution is =
**(b – a)^2 / 12** - In an empty cell formula using the maximum and minimum values you identified in steps 2 and 3.

Further reading: How to Calculate a Variance Estimator? How to Calculate a Covariance?