You're saying that a single statistic, like a "mean" or "average" is only one representation of a distribution. Many other aspects of the distribution are important, such as the variance or the mean conditional on some other factor.

Inflation is a vague concept. When people try to measure inflation, they're using filters and aggregates. Criticism that those filters and aggregations are distorting the view (for political purposes) is valid and a frequent motivation to publish academic papers.