Introduction to Experiment Indicators

Scientific experiments typically need clear indicators to measure and quantify performance. This is especially true in data-processing contexts, where several key metrics deserve close attention.
We can start with a few fundamentals familiar from high-school math: the average (mean), the mode, and the variance. The average corresponds to the "expectation" discussed in probability courses; it summarizes the overall property of a dataset in a single number. The mode is simply the value that appears most frequently. Variance indicates stability—if a dataset shows large variance, it is considered unstable.
Residual is another useful indicator. It measures the difference between data points that have a time-domain character. Residuals are particularly valuable in signal processing, where data are typically ordered by time. They are calculated by taking the difference between values at separate time points.
From residual we derive RSS (Residual Sum of Squares), also known as SSE (Sum of Squared Errors). RSS is obtained by squaring each residual and then summing the results. RMSE (Root Mean Squared Error) takes this a step further: it divides the RSS by the number of data points and then takes the square root. The result has the same magnitude as the original data and effectively represents the average residual. RMSE is especially powerful when the data contain both positive and negative values, because squaring prevents opposing residuals from canceling each other out.