Volatility is defined as the price range for a period, divided by the average price for the period:
For instance, on 2/5/2010 the average price was 122.78 with a range of 1.89, indicating a Daily Volatility of 1.5%. The Daily Volatility is obtained by dividing the daily range by the daily average. A longer Volatility period such as Weekly Volatility is obtained by dividing the weekly price range by the weekly mean price. It is important to avoid confusing this with the weekly average of the daily volatility, which is a completely different concept.
For reference, the price is plotted in red. The remaining marks on the plot correspond to the Volatility measured across several time intervals.
Investors often make a distinction between the concept of Volatility, and the concept of Risk. Academics define them to be exactly equivalent, but as can be seen here, there is good reason to distinguish between the levels of volatility or risk experienced across different time frames. Average Daily Volatility over the history of IBM has been 2% in contrast to the Average Quarterly Volatility of 20%.
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