# What is statistic in statistics?

I am getting difficulty in understanding the definition of the statistic.

From wikipedia, I come to understand that statistic is any 'information' (for example, range, mean, variance) of any sample of any given population.

Whereas in my college the definition of statistic is given as:

Suppose $$(X_1, X_2,... ,X_i,...,X_n)$$ is a random sample of size $$n$$ from any given PDF or PMF. A function $$T=t(X_1, X_2,... ,X_i,...,X_n)$$ free from unknown parameter is called a statistic.

I cannot understand the definition given in my college. Are the two definitions related to each other? What is the need of finding the statistic?

• In theory, a statistic is any kind of measurable quantity that is associated to a population (and by extension to a sample). In practice, the statistics most often used in inferential statistics are the mean, the variance, and the proportion. – Digio Oct 24 '17 at 14:08
• The two definitions you quote are more or less the same. Wikipedia is giving you helpful examples and is aimed at the lay reader whereas your class text is coming from a mathematical perspective. – mdewey Oct 24 '17 at 14:28
• This is purely a matter of notation and terminology: simply read "$t$" as "information" and "pdf or pmf" as "population." The two descriptions are then identical. The phrase "free from unknown parameter" is superfluous (do you see any unknown parameters in the arguments to $t$??). – whuber Oct 24 '17 at 15:50
• I think the main point of both definitions is that if you've got $X_1, \dots, X_n \sim \mathcal N(\mu, 1)$ it's not useful to allow your "statistic" to be $t(X_1, \dots, X_n) = \mu$. The whole point is that we need to be able to actually calculate these things, hence they need to be a function only of observable quantities. – jld Oct 24 '17 at 16:41
• A statistic is a function of a sample, a definition you will find in almost any textbook – Repmat Oct 24 '17 at 19:53