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# 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.

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.

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

#### Inputs

*Last modified Monday, 03rd October, 2022.