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?