**Syntax**

public static EStdDev Series(DataSeries ds, int period)
public EStdDev(DataSeries ds, int period, string description)

**Parameter Description**

*ds* | DataSeries used to build ESD |

*period* | Lookback period |

**Description**

Standard Deviation is the statistical measure of market volatility. If prices trade in a tight narrow trading range then

StdDev will return a low value indicating volatility is low. Conversely if prices swing wildly up and down then

StdDev returns a high value indicating volatility is high. What it does is measure how widely prices are dispersed from the average or mean price.

What makes EStdDev (exponential standard deviation) different is the use of exponential smoothing (

EMA) vs. simple averaging that takes place inside the indicator. This is believed to make the ESD bands more sensitive to the market action.

### Interpretation

- Standard deviation rises as prices become more volatile. As price action calms, standard deviation heads lower.
- Market tops accompanied by increase volatility over short periods of time, indicate nervous and indecisive traders. Or market tops with decreasing volatility over long time frames, indicate maturing bull markets.
- Market bottoms accompanied by decreased volatility over long periods of time, indicate bored and disinterested traders. Or market bottoms with increasing volatility over relatively sort time periods, indicate panic sell off.

### Remarks

- Avoid testing EStdDev of a Standard Price Series (Bars.Open, Bars.Close, etc.) for an absolute value since these series can be adjusted (split) in the future, which will change their historic deviations. Instead, normalize the test by dividing both StdDev and the value (or series) by the DataSeries value.

__Avoid__if( EStdDev.Value( bar, Close, 20 ) < 1.5 ...

__Correct__/* Normalized */
double C = Close[bar];
if( ( EStdDev.Series( Close, 20 )[bar] / C ) < ( 1.5 / C ) )...

### Calculation

Unlike

StdDev, EStdDev uses standard deviation of a population (compatible with Excel STDEVP).

Steps to calculate Extended Standard Deviation for n periods

- Calculate the extponential average price for n periods
- From each period's price subtract the mean, this gives you the deviation for each period.
- Find the sum of the squares of all deviations.
- Divide the sum of the squared deviations found in step 3 by ( n - 1 ).
- Calculate the square root of the result of the previous step.

**Example**

Please refer to

February 2017 Traders' Tip article's code.