What’s the Difference? How the Meaning Gets Twisted
A recent question about the precise meaning of “difference” led me to some past discussions of the word.
Ambiguity
Word Problems in Combinatorics: How to Misread (or Miswrite?) Them
Certain kinds of word problems tend to be easy to misinterpret or to misstate. That is particularly true in combinatorics. Let’s look at two of those, one recent and one a few years old, where we are assigning people to groups, and the wording is not quite clear.
Rolling Dice: Three Probability Problems
Last week we examined three probability problems that had problems. Looking further back, I find that Jonathan, who asked the first of those questions, asked a group of questions about rolling multiple dice in 2022. They provide some additional lessons about easy mistakes to make.
What is a Ratio, Really?
A recent question reminded me I hadn’t yet written about the complexity surrounding the definition of ratio (and related terms, like rate and fraction). Here are four questions about the words.
Algebra Word Problems: Learning from Mistakes
A recent series of questions from an insightful high school student about word problems, provided a number of opportunities to discuss how to find and correct your mistakes – or the book’s! We’ll look at five.
Probability That a Random Triangle is Acute
Some time ago we looked into the probability that a random set of sides (from, say, a broken stick) form a triangle. A recent question asked about the probability that a random triangle is acute (all angles acute) or obtuse (at least one angle obtuse), which led to more discussion of what it means for …
Implicit Differentiation: What to Do When It’s “Wrong”
(A new question of the week) Having just discussed the Chain Rule and the Product and Quotient Rules, a recent question about implicit differentiation (which we covered in depth two years ago) fits in nicely. This raises an important issue: when you get an apparently wrong answer, you may just have done something wise that …
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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.
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 »