Why Are There Different Definitions of Range?

A recent question about two interpretations of the range of a data set in statistics leads us into some older questions and some mysteries. Is “range” defined as the interval containing the data, or the difference between largest and smallest values, or 1 more than that? Yes! All three are used, and are useful.

Types of Data: Discrete, Continuous, Nominal, Ordinal, …

Last time, we looked at some ideas about appropriate graph types, and the references I found put this in the context of identifying types of data. Here we’ll look at questions about two such classifications: nominal/ordinal/cardinal (with variants), and continuous/discrete. We’ll see that classifications can become distorted as they filter down from higher levels to …

Types of Data: Discrete, Continuous, Nominal, Ordinal, … Read More »

Anything to the Zero Power: Why 1?

We’ve been looking at oddities of zero. Because “nothing” behaves differently than “something”, operations with it can be surprising. Although students learn that \(x^0=1\) for any non-zero number x, they often wonder, why?? I’ve selected a few out of at least a dozen such questions in our archive.

Is Zero Positive or Negative? Even or Odd?

Last week we looked at some basics about zero; now let’s look at whether zero is positive or negative, and then at the topic of the recent comment that triggered this series: whether zero is even or odd.

Polynomials: A Matter of Degrees

Last time we examined why polynomials are defined as they are. This time, let’s look at some tricky aspects of the concept of “degree”, mostly involving something being zero.

Polynomials: Why Are Terms What They Are?

A question last week (Hi, Zahraa!) led me to dig  up some old discussions of how we define a polynomial (or monomial, or term) and, specifically, why the exponents have to be non-negative integers. Why can we only multiply, and not divide by, variables? Since we’ve been looking at polynomials, let’s continue.

Geometric and Algebraic Meaning of Determinants

A recent question led me to look back in the Ask Dr. Math archives for questions about the definition and deeper meaning of determinants. Next week, we’ll see another old question for additional background, followed by the new question.

What are Length and Width?

One of the recent discussions I showed last week dealt with the meaning of length, and I promised more about that. Here we will look at some older questions about the ambiguity of words  like length, width, depth, and height.