A measurement is a digital quantity (to be opposed to an “information” or a “state”) captured at a given moment, once or regularly and recorded in a measurement recording system for further operations and visualization.

Measurements can represent several things depending on how they are obtained:

• A quantity directly observable at the time of the measurement (e.g., the temperature of a liquid read on a thermometer at a time t)
• Counting a number of events from the beginning (absolute value)
• Counting a number of events in a given period (The measurement only makes sense in relation to the “examination range”)
• The sum (or calculation) of a certain number of quantities at an instant t (calculated measurement)
• The sum (or calculation) of a certain number of quantities in a given period (aggregated measurement)

When observing a source for a certain amount of time a measurement can be produced.

• Sample: The examination range is zero, the measurement is instantaneous (in the source, even if it can internally represent an aggregation over time)
• Common durations: examination ranges of 1 hour, 1 day, 1 week, 1 month are commonly defined. The measurement is a calculation of a quantity that requires the observation of the source during this time (e.g. number of connections to a data service in the day).

A measurement may be taken only once, but in general it is taken at regular intervals. The sampling frequency defines the frequency of the sampling.

An aggregate measurement is a measure obtained by combining several other measurements by a aggregation function. The most common functions are counting, sum, medium. The measurements are aggregated on a aggregation space, i.e. a number of contexts that define which basic measures are included in the calculation. For example, it can be a time period or an “administrative” division.

Example of an aggregation space: Average over the month for the “Rhone Alpes” region

• 2022 Valéry Frémaux (valery@activeprolearn.com)

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