(An archive question of the week) We’ve been looking at some issues involving frequency distributions and the classes used in them. Let’s look at a related concept with some similar issues, namely the cumulative distribution function (CDF), also called an ogive (more on that name at the end of the post!).
(A new question of the week) A recent question raised a different issue about grouped frequency distributions than we have discussed previously: What do you do when the last class is labelled something like “30 or more”? As we’ll see, there is no one right answer!
Two of our most-viewed posts deal with Mode and Median of Grouped Data: how to calculate these statistics for data that is supplied in the form of frequencies for classes of data (bins), rather than the individual data values. Here we’ll complete that topic with a look at the less troublesome cases of Mean and …
We’ve been looking at measuring and drawing devices (compass, ruler, protractor); let’s move on to units of measurement. A fairly common question for students learning about measurement is, “What is the most appropriate unit for measuring ___?” The answer is not always clear, as we’ll see.
Last time we looked at how to use a ruler to measure distances. This time, we’ll consider another common question over the years: how to use a protractor to measure angles. We’ll also consider the relationship between protractors and the compass and straightedge constructions that started this series on geometry tools. And just like last …
Having just discussed why we use compass and straightedge in geometry, let’s flip that around and look at a common question at the more elementary level: How do you use a ruler to measure or draw a line of a given length? The usual issue here is working with the fractional markings on an inch …
Some time ago I looked at questions about trisecting an angle by compass and straightedge, which entailed discussing the rules for such constructions. We left open another common question: Why are such constructions important, and why do we use those particular tools? This probably isn’t explained as often as it should be. Why does it …
To finish up this long series on the order of operations, I want to look at where the “rules” came from, which will also demonstrate why some aspects are not fully agreed upon, finishing up the discussion from last time.
I want to close this series with a topic that arises constantly, both in classrooms and on social media: How do you evaluate an expression like or , where the multiplication is indicated without a specific symbol? There are several reasons one might want to interpret this differently than the rule we’ve discussed, that multiplication …
(An archive problem of the week) Last time we looked at the subtle distinction between the order of operations, which defines the meaning of an expression, and properties that allow us to do something other than what an expression literally says. Here I want to look at one longer discussion that brings out these issues …
Order of Operations: Fractions, Evaluating, and Simplifying Read More »