Average of Measurement Sequence

By Kardi Teknomo, PhD.

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In this second part of Mean and Average tutorial, I demonstrate the relationship time-average, delayed-average, moving-average and delayed-moving-average using of average composition diagram and fundamental theorem.

Suppose we have a sequence of measurement that we give notation . The index of sequence is regarded as the position of the element . We assume the index of the sequence always start at 1 and increase by natural number up to the last measurement . In this case, the sequence have a fixed length . Alternatively, the sequence can also dynamically grow over time. When the sequence grows over time, the length is not specified.

The topics are the following:

Time Average

Addition or Subtraction of Two Averages

Multiplication of Averages

Distributive Law of Averages

Delayed-Average

Moving-Average

Delayed-Moving-Average

Average Decomposition Diagram

Fundamental Relationship between Averages

Relationship of Time-Average and Moving-average

Relationship of Delayed-Average and Delayed-Moving-average

Relationship of Delayed-Average and Moving-average and Time-Average

Fundamental theorem of average

Shift Property of Average

Relationship of Delayed-Average and Delayed-Moving-Average and Time-Average

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Preferable reference for this tutorial is

Teknomo, Kardi. Mean and Average. http:\\people.revoledu.com\kardi\ tutorial\BasicMath\Average\