Recursive Time Average

By Kardi Teknomo, PhD.

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There is a better way to compute average of a sequence of large measurement data. You don’t need to store all the measurement data. All you need is to compute the current average  is the current measurement data  and the previous average . The formula is as follow

                                       (3)

Click here to see my proof of above formula

Since the subscript  start at 1, then  is undefined. For convenient, we can put zero (or any number) to give the correct answer.

Using the previous measurement data of 4, 6, 12, 9 we can get exactly the same result of average as the usual computation method, but in more efficient way. Table below show the computation using the recursive average.

The interactive program below you may type your input (only number is accepted) one at a time, then press "Input" button. To compute the time average based on your current available data. Click "Reset" button to restart. Alternatively, click "Random Input" button repeatedly to create simulated data. You need to input at least two data points to make the chart.

If you click Random input for about more than say 25 points, you will notice that the time average is not constant. The time average keeps changing over time. Compare this result with the constant average of traditional mean and average.

In the next section, you will learn the characteristic of 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