What is the term used to describe the act of estimating or inferring by projecting known information?

The term that describes the act of estimating or inferring by projecting known information is "extrapolate." Extrapolation involves taking existing data and information and extending it to predict or infer beyond that data set. This technique is often used in various fields, such as statistics, science, and forecasting, where trends observed in a limited set of data are used to make predictions about broader scenarios or future outcomes.

In contrast, the other terms listed pertain to different meanings. "Extemporaneous" refers to something that is done without prior preparation, "fastidious" describes someone who is very attentive to detail and meticulous, while "flippant" denotes a lack of seriousness, often in a context where seriousness is expected. None of these terms apply to the concept of making estimates through the projection of known information.