Dave Peterson

(Doctor Peterson) A former software engineer with degrees in math, I found my experience as a Math Doctor starting in 1998 so stimulating that in 2004 I took a new job teaching math at a community college in order to help the same sorts of people face to face. I have three adult children, and live near Rochester, N.Y. I am the author and instigator of anything on the site that is not attributed to someone else.

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.

More On Mixing Trig Functions

I’ve had several occasions in face-to-face tutoring lately to refer to a past post on mixing (that is, composition) of trig and inverse trig functions. Several recent questions have touched directly or indirectly on this same general idea and extended it, so I thought I’d post them.

Complex Powers of Complex Numbers

Having looked at issues surrounding powers and roots of complex numbers, including fractional powers, let’s go even further and consider complex powers of complex bases. Things will get a little weird as we work toward \((2+3i)^{3+2i}\)!

Powers of Roots and Roots of Powers

Last time, we looked at two recent questions about combining squares and roots, and implications for the properties of exponents. We didn’t have space for some older questions that we referred to. Here, we will go there.

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 »

When is a Line Graph Appropriate?

Graphs are used to display data. But sometimes we aren’t quite sure what sort of graph will best represent the data (or what kind of graph our teacher is expecting). We’ll look at a couple questions asking when a graph consisting of lines should or should not be used.