Statistic (Value)
A statistic is a numerical value calculated from a sample that is used to estimate a population parameter.
Definition
A statistic is a number calculated from a sample that summarizes something about it, like the average or the most common value, and is used to estimate or test claims about a population parameter. Common statistics include the sample mean ($\bar{x}$), sample standard deviation ($s$), and sample proportion ($\hat{p}$). Formally, a statistic $T(X_1, \ldots, X_n)$ is a measurable function of the sample random variables; a sufficient statistic contains all the information in the sample about $\theta$, and the Rao-Blackwell theorem states that conditioning an unbiased estimator on a sufficient statistic yields an improved (or equal) estimator.
Example
If you ask $20$ friends how many hours they sleep, the average of those $20$ answers is a statistic. A pollster who surveys $1{,}000$ voters and finds $48\%$ support a bill is reporting a sample statistic ($\hat{p}$) that estimates the true population proportion ($p$), the parameter. For exponential data, the sample mean $\bar{x}$ is a sufficient statistic for the rate parameter $\lambda$, and any other estimator can be improved by replacing it with its conditional expectation given $\bar{x}$.
Key Insight
Statistics are what we can actually measure, our window into the larger population we cannot fully see, and they are themselves random variables: each new sample produces a slightly different value, with the distribution of all possible values of a statistic called its sampling distribution. Data reduction via sufficient statistics is fundamental to efficient estimation: you lose no information about $\theta$ by summarizing the data through a sufficient statistic.