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A moving or rolling average basically is a calculation to analyze population by creating a series of mean of different subsets of the full data set. Here for examples, population of the last rolling 30 days is plotted every day. The window shifts everyday by a day, and hence we have a "moving average", it's a series.
Another example the first data point is average of last 30 day temperature. Next data point will again be average of last 30 day temperature, except that the window of the of data points has shifted by a day.
Normal average for population are just plain averages, they doesn't take into account historical data to plot. It simply is the average of population as of today.
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