Why do we need recursive formula?

Did you see the problem in the usual computation above? Suppose the device above will measure for 24 hours for a week, then you will get 7 times 24 times 60 minutes = 10,080 measurements. If the device is used to measure number of pedestrians for years, then we have so much data. As the number of data is increasing, the number of computation of the simple statistics become very large. If you have large number of data, for every measurement , you need to sum all of the data to get the average and then you need to subtract each data from the average and square them, and sum all of those square to get the variance.

Not only the number of computation become large, the memory to store all of those data also become very large. If you only need the statistics, and not the real measurement data, you still need to store all of above measurement data to compute the statistics. Is there a better way than above computation?

The answer is yes. Using recursive time average and time variance you can perform the computation much more efficient without storing all the data. Moreover, for each measurement, only a few computation need to be done.

In the next section, you will learn about recursive time average.

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These tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi. (2006) Recursive Average and Variance.
http://people.revoledu.com/kardi/tutorial/RecursiveStatistic/index.html