More About Independent Events
Last time, we looked at the basic definition of independent events. This time I want to explore some deeper questions about the concept.
What Are Independent Events?
The concept of independent events can be both very simple and easily misunderstood. We’ll be looking at several explanations of the idea, starting with the basics and then digging into some deeper questions that are often overlooked.
Cumulative Distribution Functions (Ogive)
(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!).
Grouped Data: Open-ended Classes?
(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!
Mean and Standard Deviation of Grouped Data
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 …
Choosing the Most Appropriate Unit
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.
Using a Protractor
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 …
Using a Ruler
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 …
Compass and Straightedge: Why?
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 …
Order of Operations: Historical Caveats
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.