Numerical scale definition:
A numeric (or numerical) scale, also known as a Numerical Rating Scale (NRS), is basically any scale which renders a quantitative symbolization of an attribute. This type of scale is used by presenting the respondent with an ordered set from which to choose, for example, 1 to 10, coupled with anchors. These anchors can be put at the endpoints or at each point on the scale.
The numerical presentation is used to provide the data with interval properties beyond just ordinal properties.
Choosing the best feedback mechanism or rating scale will depend on what you're trying to measure and what you hope to learn from the feedback. Numerical ratings will be appropriate for some situations while verbal comments will provide much more useful information in others.
Types of numerical scales
This has to do with ranking the extent to which a certain attribute is present (such as a classroom rank for students, or the order in which participants finished a race). So 1st and 2nd might be separated by a teeny bit, but 2nd and 3rd by a huge amount. Also, there can be no zero-eth rank.
Each number here represents an actual amount and the difference between two consecutive numbers is fixed. A zero is present in this scale, but it's not a "true" zero. For example, the temperature scale or an intelligence scale. An IQ score of zero or a temperature of zero degrees does not mean that intelligence and temperature do not exist at all.
Here, we're measuring the actual amount of something. For instance, 4 liters of water means, there's 4 actual liters of water, and 0 liters means there's no water at all. The zero has its "true" meaning.
Numerical scale example:
A tape measure is an example of a numerical scale.
Rating questions are based on the same principle, although here the scale is not always present.
One of the most well-known examples is the Pain Score, used when measuring the amount of pain a patient is enduring.