This week we look at questions about how likely it is that you can make a triangle out of three random pieces of a stick. As always in probability, the first issue comes in deciding how the process is to be done (that is, what does it mean to break a stick randomly?); we’ll also …
(A new question of the week) A good way to check (and hopefully build) a student’s depth of understanding is to assign non-routine problems, in which familiar ideas are twisted around so you have to come at them from a different direction. Here we’ll look at a question about a graph that can be solved …
I’ll close this series on averages with a quick look at the mode. Unlike the other “averages”, this doesn’t always exist, and when it is, it is not always unique. In fact, as we’ll see, sometimes we can’t be sure whether there is no mode, or many modes. How do we handle these odd cases?
(A new question of the week) Here is an intriguing question we got at the end of September from an adult whose name I’ll shorten to Arun.
In our series on averages, last week we introduced the idea of the weighted average (or weighted mean), where each item has a weight attached. The classic examples all involve grade averages in various ways. This time, we’ll look at how weighted averages arise when you need to average several averages together, something we touched …
(A new question of the week) A question in September, about graphing a horizontally-stretched cosine function, led to a long conversation. Between a typo in the problem and some inside-out thinking, this surprisingly non-routine problem led to some good mind-stretching! I have edited this down considerably by removing distractions from the main ideas, but it …
A Mind-Stretching Exercise with a Stretched Cosine Read More »
In our series on averages, we’ve looked at mean/median/mode, then at details of the (arithmetic) mean, and then at different kinds of mean (arithmetic, geometric, harmonic, quadratic). Next, I want to look at the weighted mean concept. In checking what we’ve said about this, I found a useful series of explanations of one application of …
(A new question of the week) Let’s look at a quick question from mid-September, that had a number of different answers. In some ways, this is an easy question; but we’ll take it a little further, so keep reading to the end.
Last week, we looked at exactly what the mean is, referring specifically to the arithmetic mean, the one we first learn as the “average”. But just as we previously saw that there are several things called “average” (mean, median, mode), there are in fact several different kinds of “mean”. We’ll look here at the arithmetic, …
(A new question of the week) I have often said that calculus class is where many students finally learn algebra, because now algebra is an essential tool, not just something to learn for an exam. This is especially true of a nontraditional student, who may not have taken math recently, or may even be learning …