How to describe statistics in one sentence? When I first started learning statistics, procedures like the t-test, ANOVA, chi-squared and linear regression each appeared to be very different creatures. But now I realise these procedures each do more or less the same thing. And likewise, values such as the variance, residuals, standard error and mean also measure more or less the same thing.
So I reckon all of these procedures and values, and indeed all of statistics, can be described in just one simple sentence:

What is the expected value and what is the variation around this value?

The word expected could be replaced by any of these words: hypothesised, predicted, or central.
How would other people describe statistics in one sentence? 
 A: In the words of the late Leo Breiman:

The goals in statistics are to use data to predict and to get
  information about the underlying data mechanism.

http://projecteuclid.org/euclid.ss/1009213726
A: Personally, I like the following quote from Stephen Senn in Dicing with death. Chance, Risk and Health (Cambridge University Press, 2003). I highlighted one sentence (or two) that, I believe, summarize his main point, although the whole paragraph is worth reading.

Statistics are and statistics is.
  Statistics, singular, contrary to the popular perception, is not really about facts; it is about how we know, or suspect, or believe, that something is a fact. Because knowing about things involves counting and measuring them, then, it is true, that statistics plural are part of the concern of statistics singular, which is the science of quantitative reasoning. This science has much more in common with philosophy (in particular epistemology) than it does with accounting. Statisticians are applied philosophers. Philosophers argue how many angels can dance on the head of a needle; statisticians count them.
  Or rather, count how many can probably dance. Probability is the heart of the matter, the heart of all matter if the quantum physicists can be believed. As far as the statistician is concerned this is true, whether the world is strictly deterministic as Einstein believed or whether there is a residual ineluctable indeterminacy. We can predict nothing with certainty but we can predict how uncertain our predictions will be, on average that is. Statistics is the science that tells us how.

A: 
Statistics is the science of learning from data and measuring, controlling, and communicating uncertainty.

Marie Davidian & Thomas Louis
They continue:

; and it thereby provides the navigation essential for controlling the course of scientific and societal advances

A: 
Statistics provides the reasoning and methods for producing and understanding data.

American Statistical Association
A: Statistics is a kitbag of methods and modes of thought that help people to make clear conclusions from noisy information.
A: Because we are not a godlike all-knowing creature we have to deal with uncertainty and Statistics provides methods to incorporate and reflect that uncertainty.
A: statistics is a sub-field of philosophy that deals with the following question 'how we learn from observations' using rigorous mathematical concepts.
just a side note you can make 'one sentence' very long, there is a book written by B. Hrabal that consist of one long sentence, see:
Dancing Lessons for the Advanced in Age
A: 
Statistics is both the science of uncertainty and the technology of
  extracting information from data

David J. Hand
A: Statistics is a set of logical principles and mathematical methods for summarizing quantified information in accurate, relevant ways.
A: 
Statistics is fundamentally concerned with the understanding of structure in data.

Bill Venables and Brian Ripley, first sentence in Chapter 1 of Modern Applied Statistics with S
A: Statistics provides the reasoning and methods for converting data to meaningful information.
A: In my own words
Statistics is the science of what might be

This is sort of tongue-in-cheek.
A: Fisher (1922) gave his view on the essence of statistics in the following quote (bold font added by me for the one sentence requirement):

In order to arrive at a distinct formulation of statistical problems, it is necessary to define the task which the statistician sets himself: briefly, and in its most concrete form, the object of statistical methods is the reduction of data. A quantity of data, which usually by its mere bulk is incapable of entering the mind, is to be replaced by relatively few quantities which shall adequately represent the whole, or which, in other words, shall contain as much as possible, ideally the whole, of the relevant information contained in the original data.

A: A results-oriented (and so not really descriptive) one-liner would be, for me,

Statistics is what makes the human world go round, irrespective of what is that does the same for Nature.

A: Statistics is a tool for modeling the generation of data by uncertain and/or probabilistic processes.
A: 
A name for functions of the results of observations.

from here.
This is the meaning closest to that of OP. He's not talking about the branch of science. He means statistics such as mean and median. These are the functions on data
A: Statistics is the mathematical science that allows you to figure out if the difference between sets of observations are just random or not.  
A: Statistics is about torturing data long enough until it confess anything you want to show.
I am paraphrasing Ronald Coase, see link
