Last time, we saw a summary of the difference between population and sample standard deviation, along with other differences in formulas. Here we’ll look at two short answers about the reason for that difference, and then an extensive look at why it’s true. (I’ve taken extra time and space to work through details in order …
Sample Standard Deviation as an Unbiased Estimator Read More »
Last time we introduced standard deviation. Here we’ll look into why two formulas (namely, population and sample standard deviation) are different, and why several different formulas for either are equivalent. We’ll also discover how to update the standard deviation when a new value is added. In doing so, we’ll see some different perspectives than we …
Formulas for Standard Deviation: More Than Just One! Read More »
We’ve had a number of questions about “measures of dispersion”, such as standard deviation, which tell us how much data spreads out, as opposed to “measures of central tendency”, which tell us where the middle of the data is (as we discussed in Three Kinds of “Average” and Mean, Median, Mode: Which is Best?). Why …
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.
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 …
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 …
Types of Data: Discrete, Continuous, Nominal, Ordinal, … Read More »
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.
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.
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).
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?