Sample statistics vs population statistics

[939]

Homework Statement

My task is to explain why the sample statistics I have obtained differ from the population statistics I have obtained from some data - using "concepts taught in class, if they exist". I have calculated x̄ and s, as well as σ and µ.

Homework Equations

First of all, the distribution is not normal, thus the emperical rule is invalid.

The Attempt at a Solution

Part of me thinks it's a trick question because there are very few "concepts" I can think of. The only thing I can come up with is that the mean differs because it is merely one sample, and according to the Central Limit Theorum, if I had a bigger sample space, the mean would be similar. Similarly, the standard deviation differs because it is merely one sample. Is this all there is to it or am I missing something?

 

[camillio]

Sample statistics are obtained by sampling from a population. The idea is that the statistical properties of a population can (usually) be only estimated. In this respect, I slightly doubt about your data-based \mu, \sigma^2 :-)