*Section author: Danielle J. Navarro and David R. Foxcroft*

# Estimating unknown quantities from a sample¶

At the start of the last chapter I highlighted the critical distinction between
*descriptive statistics* and *inferential statistics*. As discussed in
Descriptive statistics, the role of descriptive
statistics is to concisely summarise what we *do* know. In contrast, the
purpose of inferential statistics is to “learn what we do not know from what we
do”. Now that we have a foundation in probability theory we are in a good
position to think about the problem of statistical inference. What kinds of
things would we like to learn about? And how do we learn them? These are the
questions that lie at the heart of inferential statistics, and they are
traditionally divided into two “big ideas”: estimation and hypothesis testing.
The goal in this chapter is to introduce the first of these big ideas,
estimation theory, but I’m going to witter on about sampling theory first
because estimation theory doesn’t make sense until you understand sampling. As
a consequence, this chapter divides naturally into two parts Samples,
populations and sampling through Sampling
distributions and the central limit theorem are focused on
sampling theory, and Estimating means and standard deviations and Estimating a confidence interval make use of sampling theory to discuss how statisticians
think about estimation.