Binary compression of continuous data
“Which am I supposed to use: mean or median?” Early on in my stats classes, we talk about how to describe the distribution of a piece of numerical information — things like height, weight, age, income, and so on that can vary continuously. A good description should cover three aspects of the distribution: A measure […]
Dispersity in the classroom
Here’s an amusing way dispersity, a measure of how different the sizes of objects in a collection are, crops up in classroom management. Imagine that I’m a teacher who wants more participation in class. More specifically, during class discussions a few of my students are regular contributors, but I want everyone to join in on […]
Spontaneous Inequality
A fun problem making the mathematical rounds: if you give everybody some number of dollars (say you give 45 people $45 each), and at every tick of the clock everyone with money chooses one random person $1, how will the money eventually end up distributed? You might think it’ll stay approximately equal—”approximately” only because of […]
“Genie” Coefficient
Optimization Metrics
Clara and I have to take a written exam in order to transfer our driver’s licenses to Minnesota, so we’re studying the Minnesota driver’s manual. In the section on crosswalks I found this instruction: The problem is that you can’t leave an intersection both as quickly as possible AND as safely as possible. To leave […]