Std / List Layer

Calculate the standard deviation of numeric lists. Similar to numpy.std() or R's sd(). Returns the sample (n-1) or population (n) standard deviation. Supports lists of different lengths.

Mathematical definition: For a list of values $x_1,x_2,...,x_n$ with mean $\mu =\frac{1}{n}{\sum }_{i=1}^n{x}_i$:

Population standard deviation (ddof=0): $$\sigma =\sqrt{\frac{1}{n}\sum _{i=1}^n(x_i-\mu {)}^2}$$

Sample standard deviation (ddof=1): $$s=\sqrt{\frac{1}{n-1}\sum _{i=1}^n(x_i-\mu {)}^2}$$

Example transformation:

Common applications:

• Analyzing price volatility in financial data
• Measuring sensor reading stability in IoT
• Detecting anomalous patterns in metrics
• Computing confidence intervals in statistics
• Evaluating process consistency in manufacturing
• Analyzing performance variation in systems

Note: Only works with numeric lists. Lists with fewer than 2 elements return null. Null values are ignored in calculation. The choice between population (ddof=0) and sample (ddof=1) depends on whether the data represents an entire population or a sample.