Scales of Measurement when we use the term " scales of measurement", what do we mean 


*

*by scale 

*by Measurement
?
As far i know, measurement denotes "a value" and scale denotes "the unit" of the value.
So if i say, the age of a child is $5$ years, then here


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*"year" is the  scale

*"$5$" is the  Measurement
Is that the case?
But in an article it is written that 
"Scaling is a procedure for the assignment of numbers to a property of objects."
It seems to me "$5$" is the scale in the particular example of $5$ years of a child.
 A: Scale is usually a range or a metric of measurement that everything fits in to avoid large calculations and better visualize the data using a reference point.
The age "5 years old" is not a scale. Year is the metric used not the scale. The scale is "when your born to the maximum amount of years a person can live"
A common use of scaling is changing data to a Log scale so you can easily visualize larger ranges of data for things growth and magnitude.
A: "Scale" in that context might have a couple of different meanings depending on the background of the person stating that, and "measurement" can really mean many different things. This is just to say that I don't think there is an unequivocal interpretation to that sentence, especially without more context.
Having said that, one of the most important theories of measurement concerned with the concept of scale is the representational theory of measurement. A simple starting point to this theory is the 1946 article by S.S. Stevens "On the Theory of Scales of Measurement", where he lays out what is now considered a commonplace definition throughout psychology and psychometrics: "Measurement, in the broadest sense, is defined as the assignment of numerals to objects or events according to rules" (p. 677). In his paper, Stevens also implicitly defines scales as the kind of isomorphisms that can be established between, roughly speaking, the objects being measured and the numerical representation that is being used to model their relations. Based on these distinctions, Stevens introduced in this paper the taxonomy of scales of measurement that includes Nominal, Ordinal, Interval and Ratio scales based on their mathematical group structure.
Long story short, from the standpoint of this theory, my best guess is that the statement "scaling is a procedure for the assignment of numbers to a property of objects", is conflating the meaning of measurement and the meaning of scale. I am hard pressed to think of any theory of measurement under which "5" could be considered a scale, even if you are making the concept of unit and scale synonymous (which are separate and play different roles on different measurement theories). Your first statement, that "year" is the scale and "5" the measurement seems to be parallel another famous definition of measurement based on Maxwell's definition of physical quantity as a pure number (5 in your case) and a unit (year), however, notice that his definition is not predicated on the concept of scale.
A couple of additional points. Stevens' paper is usually considered the main starting point of the representational theory of measurement, but this theory has been improved and developed extensively afterwards. The common reference for the current understanding of this theory is the three volume work "Foundations of Measurement", starting with the 1971 volume by Krantz, Suppes, Luce and Tversky. An accessible and brief introduction to this theory can be found in Narens's (1986) article "Measurement: The theory of numerical assignments".
Finally, it is worth remembering that this approach to measurement is not the only definition of the concept of measurement (see for instance the definitions in metrology, or the classical theory of measurement) and therefore it is not without its critics. For an overview of different approaches in psychometrics you can see, for instance, Borsboom's (2005) "Measuring the mind : conceptual issues in contemporary psychometrics". 
