# Technical Studies Reference

### Z-Score

This study calculates and displays the Z-Score of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data Input, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Inputs Mean Length and Standard Deviation Length be denoted as $$n_{\mu}$$ and $$n_{\sigma}$$, respectively. Then we denote the Z-Score at Index $$t$$ for the given Inputs as $$Z_t(X,n_{\mu},n_{\sigma})$$, and we compute it in terms of a Simple Moving Average and a Standard Deviation for $$t \geq \max\{n_{\mu},n_{\sigma}\} - 1$$ as follows.

$$\displaystyle{Z_t(X,n_{\mu},n_{\sigma}) = \frac{X_t - MA_t(X,n_{\mu})}{\sigma_t(X,n_{\sigma})}}$$