For a variable X following a probability law, the definition of sample mean xbar is an important statistical concept. Is the sample mean a property of Statistics, or of Mathematics?
I'm confused by the question. The body of knowledge in Statistical analysis is a subset of Mathematics. Most analysis techniques seen in Statistics often derive from analysis in pure mathematics or applied mathematics, so I am not sure what you're asking. Can you elaborate a bit more, and I'm sure others will be able to answer.
Hope this helps :)!
An estimator of μ=E(X) is the xbar=(1⁄n)∑xi
It is an unbiased and consistent estimator of E(X).
So, it is statistical, but since Statistics is a branch of Mathematics, it is also a mathematical property.
(The concept of a consistent estimator is defined with limits, ie maths.)
As mentioned below the sample mean can be defined as an estimator of the mathematical expectation. It can also be defined in an geometrical way as the point minimizing the sum of squared distances to all the sample points.
Perhaps the way I had framed the question was found to be a bit confusing!
What I actually meant is as what follows. In the realm of Statistics, almost all field studies, at least initially, are geared to finding the sample mean. Therefore, apparently it looks as though the concept of sample mean is a property of Statistics, in the sense that the statistics fraternity owns it.
However, we need to apply the theory of affine spaces to define degrees of freedom necessary to work out all statistical analysis that can be done with reference to the collected data, because degrees of freedom associated with the data and the dimension of the concerned affine space are of the same meaning. Therefore, before being a property of Statistics, the sample means should actually be a property of Mathematics. This was the central idea of my question.
Of course, yes, the concept of centre of gravity is the same as the concept of sample mean.
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