The cost of a calmer signal

A smoother line can be easier to read and slower to tell you what changed.

A moving average takes the most recent measurements and gives each one equal weight. Random fluctuations tend to cancel out, so the estimate becomes less jumpy. The window size controls how many readings contribute.

There is a cost. When the underlying signal turns, older measurements still pull the average in the previous direction. A wider window reduces noise but makes the estimate respond more slowly. Smoothing does not give you certainty for free.

Try the signal experiment with no noise and a wide window. The measurements are already perfect, yet the estimate still lags. Then add noise and reduce the window. Choosing a useful setting means balancing two things: how much variation you can tolerate and how quickly you need to notice a change.