A sample mean is not the same as a concept’s conceptual midpoint.

Evidence

From a semantic perspective, the approach is troubling. The standardization approach defines extreme values in terms of their relationship to the sample mean, which is treated as the “middle point.” But from a semantic point of view, the sample mean may, or may not, represent the middle point of a concept. The middle point corresponds to the conceptual middle value. For instance, with the Polity scale, which ranges from − 10 to 10, the conceptual middle point might be 0.4 By contrast, the sample mean for Polity is about + 3. — Gary Goertz, Social Science Concepts and Measurement, 867

Categorization

• XREF: Polity’s scale −10 to +10 with conceptual midpoint 0 echoes the ordinal-scale discussion and connects to any dataset built on a defined neutral point.