2 Dispersion - why measure spread?
The average is an important way of summarising information in a single value, and you (or your learners) can already tackle some interesting questions. What is the average temperature at the North Pole? On average, does your favourite sports team do better at home, or away?
However, the average is only one character in a statistical story.
Here are the points scores of two local rugby teams in their last five matches, listed in ascending order. Which team is better?
Team A: 15, 18, 18, 19, 23 Team B: 7, 11, 18, 24, 33
Both teams have the same mean (18.6) and the same median (18) – so it is fair to say that they have the same average score. However, team A is more consistent than B, since the values are more clustered around the average. If you want a reliable or predictable performance, team A is better; but team B might surprise you with a particularly good game, or a bad one!
The focus of this section, the range, is not an average. Instead, it is a way of reporting the spread (or dispersion) of a data set.
Note that, just as here, averages and range often get taught together and practice questions involve repeatedly calculating the mean, median, mode and range of many sets of numbers. Due to this, learners often mistakenly refer to the range as an average because they do not see the meaning behind the calculations. Teaching what an average represents (a measure of location), what range represents (a measure of dispersion) and using contextual questions for practice helps give meaning.