Is confirmatory vs exploratory statistics "induction vs deduction"? This webpage says:  

Inferential Statistics - Deductive Approach
Descriptive Statistics - Inductive Approach

But I doubt it. If I understand correctly, 


*

*Inferential Statistics is "given some data, find the probability model that generates the data", so it is a specific-to-general logic process, and therefore it is induction.

*Descriptive Statistics is "given some data, represent the data in another way", so it is specific-to-specific process of changing data's representation. So it is neither induction or deduction.
Am I wrong? 
 A: I don't think either the web-page or your statements are correct. I'd rather stick with more straightforward descriptions:
Inferential statistics: Given a sample, what can we say about the population from which it was drawn?
Descriptive statistics: Given a sample, what can we say about the sample?
Both can be used as part of inductive or deductive reasoning - the type of reasoning is not supplied by the statistics. 
A: To add to @Peter Flom's answer, it is worth defining the other terms that were used:
Deductive reasoning:  Derive conclusions or predictions about specific cases from fundamental rules or theories.
Inductive reasoning:  Derive universal rules or theories from observation of many cases.
Inferential statistics use both inductive and deductive reasoning.  You are trying to establish rules about the behaviour of a system based on evidence, but you are testing models against probability theories derived deductively (i.e., probability distributions in parametric models or the combinatorics that are the basis of non-parametric models).
Descriptive statistics don't really qualify as "reasoning" in my book.  Saying the average of something is x and the standard deviation is s isn't any more of an argument than saying the colour of something is blue.  You're describing what you have in front of you, not drawing any conclusions beyond it.
