# Numeric variables with long-tail distributions

**auto** which bins values into equal ranges. You can set "Round by..." to **log** for distributions with heavy tails. Learn more about the "Round by..." dialog in our "Bin numeric values" tutorial.

Protobi automatically bins numeric variables into ranges. Numeric variables come in a few varieties:

- Constants (e.g. π = 3.141... )
- Light-tailed distributions
- Heavy-tailed distributions

Many variables we encounter in market research have light-tailed or even distributions, such as percentages, preference ratings, etc.

Other variables such as number of patients, income, book sales, frequent flier miles, etc. have heavy-tail distributions. Benoit Mandelbrot coined the terms "mild" versus "wild" randomness to describe the difference.

## Example

Below is an example where customers are asked for their purchase budget in dollars. This has a classic heavy-tail distribution with a small number of individuals with very large values.

By default, Protobi sets Round By = **auto**, which chooses linear bin sizes for numeric variables based on the standard deviation. We can see that many people have budgets of $1,000 to $5,000, and very few have budgets much over $30,000.

The second version uses default binning with Round By set to **log** ,which chooses logarithmic bin sizes. In the graph below we can see that there are quite a number of customers willing to spend under $1,000, and also a substantial number that are willing to spend a lot more.

A product strategy might be radically different with this perspective, selling differently to customers with $250 versus $2,500 to spend, rather than lumping them all into an "Under $5,000" category.