The cumulative mean, also known as the running mean or moving average, provides us with a dynamic view of how the average value of a dataset changes as new observations are added incrementally. It is an invaluable tool in time-series analysis, trend identification, and smoothing noisy data.
Imagine you have a series of numeric values, and you want to find the average of the first observation, then the average of the first two observations, followed by the average of the first three, and so on. This iterative process generates the cumulative mean, painting a picture of how the data behaves over time.
Often times, we care about the moving average over a specific window, such as the last n periods. This particular post covers the moving average over the entire set of data.