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? …
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 …
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 …
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, …
Last week, we started a series on averages, looking at a common list of three kinds of average: the mean, median, and mode. This time, we’ll focus in on the (arithmetic) mean, thinking about why it is appropriate for many applications; that will lead into next week’s discussion of when other kinds of mean are …
There are three different statistics that are commonly taught as “averages”, or “measures of central tendency”, of a set of numbers: mean, median, and mode. (There are others as well, which we will get to later.) What are they? How do they differ? How do you use them? We’ll look into questions like these as …
(A new question of the week) A recent question (from May) about approximating the binomial distribution with the normal distribution led to some (accidental and otherwise) insights about the method. I have to solve this problem: A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. The plan …
News about testing for viruses has reminded me of a couple problems that I linked to some time ago, but never dealt with directly. The question is, given data such as the result of a (fallible) blood or swab test, how sure can we be of the results? The answer is sometimes surprising. False positives …
(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!). What is an ogive? …
(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! An open question Here is the initial question, which …