I will give you two situations where the grand mean will lead you astray. The point is, you need to always consider the 'who' part of the question before you begin to look at measures.
Pareto Principle. The majority of effect comes from a minority of the people (aka 80/20 rule).
Differentiation -- always starts with the question: for whom?
The first situation is one where a large provider competes across several segments within a market. They have many smaller competitors, most of whom specialize in only one or two segments. Based on my experience at HP researching competitive dealer value propositions for the copier channel.
The second situation is based on my work with the BEST Places to Work in Idaho. When employers only focus on the Grand Mean (overall average), they end up creating a workplace that best suits the majority of their workforce. On the surface you might say this sounds like a good idea. But once you consider the Pareto Principle, you should realize that by pleasing the majority will ignore and often displease the valuable 20%.
These employers may have no problem filling positions for the 80%, but could be struggling when it comes to finding, hiring, and keeping those that fall in the valuable 20%