4.5 Summary

It sure feels like we’ve covered a lot! You might need a recap. You will find it below.

The measures of dispersion tell us how a variable’s cases are distributed: whether they are more tightly clustered together, or more loosely spread out. After all, it’s perfectly possible to have two variables with the same central tendency measures but with different measures of dispersion!

There are four measures of dispersion that are typically used: range, interquartile range (IQR), variance, and standard deviation. While the former two are simple and account for the dispersion of cases only through the positioning of a few cases in the (ordered) distribution, the latter two employ all cases’s values to produce somewhat more complicated and comprehensive measures of a variable’s spread.

The range reports the difference between the highest and the lowest values. The IQR provides the same but for the middle half of the cases. The variance calculates something like an average of the squared distances of all cases from the mean (in squared terms), while the standard deviation, through square-rooting the variance, provides us with an almost-average of the distances of all cases from the mean (in standard — i.e., regular — units). Generally, the larger the measures of dispersion, the more variability the variable has.

Finally, as they all require numerical values, all measures of dispersion are applicable only to interval/ratio variables: we cannot provide dispersion measures for nominal or ordinal variables.

With this, we have the full range of measures to describe variables: we not only learned how to graph variables to see their distribution visually, but also to calculate how their cases cluster (through the three measures of central tendency, the mode, the median, and the mean) and how the cases can spread (through the four measures of dispersion, the range, the interquartile range, the variance, and the standard deviation).

We also learned that while we can graph all types of variables, the measures of central tendency and dispersion vary in their applicability depending on a variable’s level of measurement. While the mode applies to all variables, and the median to ordinal and interval/ratio variables, the mean, the range, the IQR, the variance, and the standard deviation apply only to interval/ratio variables. Keep this in mind when deciding what kind of information to provide about a specific variable.^[1] 

Before we continue inching toward inferential statistics, starting with the normal curve and basic of probability in Chapter 5, here is a handy list of things you should know before proceeding further.