ME$021-$ Engineering Computing $-$ Fall $2024$

Assignment HW $03$b

"Moving Averages"

Moving averages are a way of filtering data, often used to "smooth" spikes or random fluctuations in the data.

There are several methods of generating a moving average from a raw data set. For our purposes, the moving

average at an index will be the average of the data at that index and the data within an "index radius" $($or

sometimes "window half$-$size"$)$ of that data. The radius can generally be any non$-$negative integer. If the radius is

$0,$ then the moving average is the same as the data, because we are averaging that data point with that $0$ points

before and after it$.$ With a radius of $1,$ each moving average point would be the data at that point averaged with

the data one point before and one point after it$.$ Et cetera.

Obvious question: What do we do near the first and last points in the data set, where the radius would have us

include data points in the average that aren't in the data? For example, with a radius of $2,$ the moving average for

the first data point should include that data point averaged with the two points before it and two points after it$.$

But, there aren't two points before it$.$ And, for the second data point, there is only one point before it$,$ so there is

no way to use the two points before it$.$ A similar issue would exist for the last two data points in the set. For our

purposes, we do not average in points that are not in the data set, just using those that are.

An example moving average for a set of $10$ data points using a radius of $2$ is shown below, along with the details

of how the calculations are done. Notice that the averages for the first two and last two points are calculated

differently, as explained above.