# Variability

## What it is:

Variability is the degree to which a data series deviates from its mean (or in the accounting world, how much a budgeted value differs from an actual value).

## How it works (Example):

For example, let's say Company XYZ stock has the following prices: The average of these prices is \$21.33. To calculate the variance, we see how "far away" each day's stock price is from \$21.33, like this: Notice that some of the differences are negative. Because we're going to calculate the average difference, the negative numbers create a mathematical problem (they'll offset the positive numbers and screw up the calculation). To avoid this, we square each difference so that each difference is positive, like this: The last step is simply calculating the average of those squared differences, which is \$9.42, and then taking the square root of that number to get the amount by which Company XYZ stock tends to vary from its average price.

The square root is \$3.07, meaning that when Company XYZ deviates from that \$21 average, it tends to do so by about \$3.07.

## Why it Matters:

This is only one way to measure variability. Beta, regression analysis, and many other statistical methods are designed to figure out just how volatile a data series is. Variability is a measure of volatility and thus a measure of risk, because it measures how much something like a stock tends to deviate from its "usual" value. The higher the variability, the more wildly the stock fluctuates when it fluctuates. Accordingly, the higher the variability, the riskier the stock.