User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

To do:

Disambiguate Class

Empty class

Class width

Class mark

Class limit

Class boundary

Frequency

Relative Frequency

--GFauxPas (talk) 21:52, 5 October 2012 (UTC)

Let $S$ be a sample or a (finite?) population.

Let $\omega$ be a qualitative variable, or a class of a quantitative variable

The frequency of $\omega$ is the number of individuals satisfying $\omega$.

(Here I start making things up)

It can be understood as a mapping:


 * $\operatorname{freq}:\mathcal P\left({S}\right) \to \N$:


 * $\operatorname{freq}\left({\omega}\right) = \left \vert \left\{{x \in S : \omega \left({x}\right) }\right\}\right \vert$

Or something. My books don't explicitly define frequency as a mapping but it clearly is. I have to think about how to define such a mapping rigorously, and am welcome to suggestions. --GFauxPas (talk) 20:15, 7 October 2012 (UTC)


 * It might not be a mapping as such because there is probably a proper class of qualitative variables. Your picking of $\mathcal P \left({S}\right)$ as a domain yields a potentially obscuring identification of qualitative variables having the same extent (elements $x$ satisfying it).
 * I would also say that if $R$ were a quantitative variable then the variable checking if $R = r$ ($r$ as appropriate) should be considered qualitative (same for variables testing if $R$ is a member of some interval or set of results). You could try:
 * "Suppose $X$ is a (the?) collection of (meaningful) quantitative variables on the sample/population $S$. Then $\operatorname{freq}$ ... blabla"
 * to surpass such technical intricacies and get down to the stuff you are interested in. Of course, you can play around with the words, I think you'll get the idea. --Lord_Farin (talk) 21:31, 7 October 2012 (UTC)


 * Should I get rid of the first criterion defining qualitative variable? I added it because otherwise every quantitative variable is also qualitative, and the books I've seen assume that that is not the case. Though the definition of class allows the intervals to be singletons. Perhaps it's best to define the frequency as "the number of individuals satisfying $\omega$" full stop. More set/class theoretical definitions can be created if a definition or theorem requires one. --GFauxPas (talk) 21:53, 7 October 2012 (UTC)


 * It seems perfectly fine as it stands; your last suggestion seems like the best way to go. We shouldn't make a dash for rigour if we compromise correctness. --Lord_Farin (talk) 07:18, 8 October 2012 (UTC)