Last time, we considered what the normal distribution and the z-score mean; here, we’ll look at some more recent questions demonstrating how to use them. In particular, we’ll see basic examples using a table, and then decide what to do when the right number isn’t there.
Last time we looked at some questions about drawing or interpreting the normal curve (graph of the normal distribution). Let’s back up and consider what it actually is. In particular, we’ll see what the “z-score” means.
We’ll look here at a recent question, and another from a year ago that it reminded me of. I see a lot of inaccurate sketches of the normal distribution, usually from statistics students (in which case accuracy isn’t really important, but can show that you know what you’re talking about), and sometimes elsewhere.
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.