Enter the total variance and the mean of the set into the Calculator. The calculator will evaluate the Index of Dispersion. 

Index of Dispersion Formula

IOD = V / m


  • IOD is the Index of Dispersion ()
  • V is the total variance
  • m is the mean of the set

To calculate Index of Dispersion, divide the total variance by the mean of the set.

How to Calculate Index of Dispersion?

The following steps outline how to calculate the Index Of Dispersion.

  1. First, determine the total variance. 
  2. Next, determine the mean of the set. 
  3. Next, gather the formula from above = IOD = V / m.
  4. Finally, calculate the Index of Dispersion.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

total variance = 2.5

mean of the set = 60


What is the Index of Dispersion used for?

The Index of Dispersion is used to measure the variability or dispersion of a set of data relative to its mean. It helps in understanding how spread out the data points are, which is crucial for statistical analysis and decision making.

How does the Index of Dispersion differ from standard deviation?

While both the Index of Dispersion and standard deviation measure the spread of data, the Index of Dispersion is a ratio of variance to mean, making it dimensionless. In contrast, standard deviation provides the spread in the same units as the data, which can be more intuitive for understanding variability.

Can the Index of Dispersion be negative?

No, the Index of Dispersion cannot be negative because it is derived from the variance, which is always non-negative, and the mean, which is assumed to be positive in this context. A negative Index of Dispersion would indicate incorrect data or calculations.

Why is it important to calculate the Index of Dispersion?

Calculating the Index of Dispersion is important because it provides insights into the distribution of data points around the mean. It can help identify if the data is overdispersed or underdispersed, which has implications for model selection, hypothesis testing, and understanding the underlying processes generating the data.