Statistics

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.

What is Adjusted Frequency in a Histogram?

Some time ago we looked into the meaning of histograms, on the way to the concept of the Probability Density Function. A recent question focused on the histogram itself, in a way that will add to that discussion. We’ll learn about frequency density, which was overlooked there, and discover an alternative way to label a …

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 …

When is a Line Graph Appropriate?

Graphs are used to display data. But sometimes we aren’t quite sure what sort of graph will best represent the data (or what kind of graph our teacher is expecting). We’ll look at a couple questions asking when a graph consisting of lines should or should not be used.

Boxes, Whiskers, and Outliers

Last week we looked at one way to display data, the stem-and-leaf plot. This time, we’ll look at a very different one, the box-and-whisker plot, which summarizes the data more broadly.

Stems, Leaves, and Data

It’s been a while since we’ve written about statistics, so I want to start a short series about that. Here, we’ll look into stem-and-leaf plots (also called stemplots).

One Mode, No Modes, Many Modes

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?

Weighted Averages: Averaging Averages or Rates

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 …