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# Technical Studies Reference

### Standard Deviation

This study calculates and displays a moving Standard Deviation of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_i$$ be the value of the Input Data at Index $$i$$. Let the Input Length be denoted as $$n$$. Then we denote the Variance at Index $$t$$ for the given Inputs as $$Var_t(X,n)$$, and we compute it for $$t \geq n$$ as follows.

$$\displaystyle{Var_t(X,n) = \left.\left(\sum_{i = t - n + 1}^tX_i^2\right) \middle/ n\right. - \left(\left.\left(\sum_{i = t - n + 1}^tX_i\right) \middle/ n\right.\right)^2}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.

The Standard Deviation at Index $$t$$ for the given Inputs is denoted as $$\sigma(X,n)$$, and we compute it in terms of the Variance as follows.

$$\sigma_t(X,n) = \sqrt{Var_t(X,n)}$$

In the above formula, the symbol $$\sigma$$ is the lowercase Greek letter sigma.

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through File >> Open Spreadsheet.

*Last modified Wednesday, 03rd January, 2018.