However, as you increase the sample size, you have more opportunities to obtain these extreme values. In general, you are less likely to observe extreme values. If one of those numbers is unusually high or low, it affects the entire range even if it is atypical.Īdditionally, the size of the dataset affects the range. While the range is easy to understand, it is based on only the two most extreme values in the dataset, which makes it very susceptible to outliers. Dataset 2 has a broader range and, hence, more variability than dataset 1. For example, in the two datasets below, dataset 1 has a range of 20 – 38 = 18 while dataset 2 has a range of 11 – 52 = 41. The range of a dataset is the difference between the largest and smallest values in that dataset. Let’s start with the range because it is the most straightforward measure of variability to calculate and the simplest to understand. Now, let’s move on to the different ways of measuring variability! Range
We also need to understand the variability around the middle of the distribution to get the full picture. The parts that come off an assembly line might appear to be identical, but they have subtly different lengths and widths.Īs this example shows, the central tendency doesn’t provide complete information. When you order a favorite dish at a restaurant repeatedly, it isn’t exactly the same each time. Your commute time to work varies a bit every day. Understanding that variability around the mean provides critical information.
In some situations, extreme values can cause problems! Have you seen a weather report where the meteorologist shows extreme heat and drought in one area and flooding in another? It would be nice to average those together! Frequently, we feel discomfort at the extremes more than the mean.
Consequently, understanding variability helps you grasp the likelihood of unusual events. However, when the variability is higher, the data points are more dissimilar and extreme values become more likely. When a distribution has lower variability, the values in a dataset are more consistent. While the mean is relevant, people often react to variability even more. Analysts frequently use the mean to summarize the center of a population or a process. Let’s take a step back and first get a handle on why understanding variability is so essential. Why Understanding Variability is Important