How should a mathematically-inclined person learn descriptive statistics?

I share your concern about studying non-mathematical subjects, but when I have to face a decision like this I ask myself: what for? I guess that you have in mind a specific pattern if you ponder over this choice. Could this subject be useful for what you have in mind? I don't really think that studying something apart from mathematics is bound to be a loss of time: also descriptional/qualitative science can result in a better understanding of phenomena hardly investigable mathematically. And from this enhanced understanding can come an improved mathematical model that can answer the questions not satisfied by your qualitative model.

Of course I would prefer a mathematical subject if an (almost) equivalent one existed and I bet you too.

Descriptive statistics is a part of mathematics, but it is generally thought at high school. It is not useful to mathematicians. This also gives the reasons why there is no book:

1. Most mathematicians are not willing to write a book.
2. There is no real need for a book since most mathematicians don't want to study it.
3. People who need it, usually don't like rigorous mathematics.
4. Descriptive statistics is usually in high school books, where it is combined with algebra, geometry and other subjects.

However, you need descriptive statistics to give your information as clearly as possible. For example, when you want to show how many per cent of the tax money is spent at each category, a pie chart is useful. When you want to compare the amount of tax paid per country, a bar chart may be more useful.

The mathematical part of descriptive statistics is learning about how to compute or create all those diagrams or central tendencies. This is not hard: The formulas are actually easy, and creating diagrams is more learning how to use software than learning maths. The non-mathematical part is deciding between all those diagrams and statistics. This is actually the harder part for a mathematician.