Statistics

Four Kinds of “Mean”

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, …

Four Kinds of “Mean” Read More »

Making the Mean More Meaningful

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 …

Making the Mean More Meaningful Read More »

Three Kinds of “Average”

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 …

Three Kinds of “Average” Read More »

Normal Approximation … or Not?

(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 …

Normal Approximation … or Not? Read More »

Bayes and Virus Testing

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 …

Bayes and Virus Testing Read More »

More Than 100 Percent?

One of the questions we looked at in our recent survey of percent change problems involved percentages over 100%, which often confuse students. How can anything be more than 100%? Let’s look at a couple questions about that issue. No such thing? Take this question from 1999: More Than 100 Percent Please help to settle …

More Than 100 Percent? Read More »