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TAI - Standard Deviation

 

Name, Sometimes Called:

Standard Deviation
In statistics, its symbol is the lower case Greek letter sigma (sigma).

Brief Description:

The standard deviation is a statistical measure of dispersion, or volatility in TA terms. It is used as a component of other TAIs, such as Bollinger Bands.

Definitions, Formulas:

The standard deviation measures dispersion, scatter, or volatility. It provides a measure of how the raw data is distributed around a simple moving average or mean.

Begin by selecting the interval for the data to be examined. We use N = 20.

Then calculate the average (mean) closing price (SMA) of the N price values
Equation

The calculation for the (sample) standard deviation is then

Equation

where

SN = the (20-day sample) standard deviation
X sub i = each of the 20 closing price values

Positive Development Calculation:

For this TAI, there is no positive development (NPD). It is used as a component of other TAIs, such as Bollinger Bands as well as a measure of volatility.

History:

The standard deviation is a statistical measure with a long history. Karl Pearson, sometimes called the father of modern statistics, reportedly introduced the term “standard deviation” in 1893, although the concept was by then over a century old.

High standard deviation values indicate widely dispersed data (drastically changing prices). Conversely, low values indicate relatively stable prices.


This chart below shows the standard deviation indicator applied to the closing price of Panera Bread (PNRA) from September 2003 through September 2005. Notice the high points near point A on the Standard Deviation line. Remember that standard deviation is a measure of volatility, not direction. The peak over 3 standard deviations to the left of A were on a price rise. The slightly higher peak to the right of the A were on a price decline.

What constitutes “high” or “low” volatility is somewhat subjective. Generally standard deviations from zero to one contain 68% of a given population. From zero to two contain 95%, and zero to three about 99%. Therefore anything above three is very rare and very volatile. Anything above two is more volatile than anything below one.

 

 
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