# Standard Deviation

The standard deviation is a mathematical formula for the average distance from the average.  This tells you how spread out a group of items is.

We don’t care about the actual position of the points.  Imagine we have two lists of stock prices.  A = (\$1.02, 1.04, 1.05, 1.05, 1.06), B = (\$100.02, 100.04, 100.05, 100.05, 100.06).  A and B both have the same standard deviation, approximately 1.36 cents.  In both lists, the average distance between the each price in the list and the middle of the list is about \$0.0136.

The order of the prints does not matter.  The standard deviation of (\$1.06, 1.05, 1.02, 1.04, 1.05) is also \$0.0136.  The formula for volatility is very similar to the formula for the standard deviation, but volatility takes order into account.

Repetition is important.  If we say C = (\$1.02, 1.02, 1.02, 1.04, 1.05, 1.02, 1.06), we will get a different standard deviation.  Even though C and A have the same prices, some appear more in one list and some appear more in the other.  We assume that 1.02 is more important in list C than in list A.  This allows us to minimize the effects of any one print, and focus on the more common prices.

The standard deviation is often used to model noise.  We might said that A and B have the same noise, if you only look at dollars.  More often, we would say that A is a lot nosier than B because the standard deviation of A is a much larger percentage of the values A.

At first glance this may sound complicated, but traders use this concept all the time.  Stock charts almost never start from \$0.  Instead, the bottom of the stock chart is near the lowest price, and the top of the chart is near the highest price.  By looking at the range of prices on the left axis of the chart, you can get an idea of the standard deviation of the stock prices.  The actual formula for standard deviation is more precise than this — it takes every point into consideration not just the high and low — but the basic idea is the same.

We use standard deviations ubiquitously in the alerts server.  When comparing a recent price action for a stock to the history of that same stock, you need precise measurements of how much the stock usually moves.  It is not enough just to know the high and the low.

Some traders use the term “Standard Deviations” synonymously with “Volatility”, because the formula for volatility uses standard deviations.  For example, Bright Bands report when a stock moves a specific number of standard deviations away from the previous close.  Note that this term is not very precise, and usually needs some additional details.  In the case of Bright Bands, for example, we should point out that we scale the volatility so that one standard deviation is a normal amount for a stock to move in one day.