4.8 – Choosing a Measure of Spread

Which measure of spread (range, variance, standard deviation) should I choose to describe the variability of a group of scores?

Choose standard deviation. It’s as simple as that. The standard deviation is our best measure of spread. It is dependent upon every score in the distribution and provides an excellent measure of spread. The result tells us how much all the scores in a group deviate on average from the mean for that group. If a group of scores doesn’t deviate much at all, for example, has a standard deviation of closer to 0 such as 1.5, then we know that the group of scores deviates from the mean by an average of 1.5 points, and thus are not very different from each other or the mean. However, if a group of scores deviates a good bit, for example, has a standard deviation that is much larger such as 28.35, then we know that the group of scores deviates from the mean by an average of 28.35 points, and thus are pretty different from each other or the mean.

Why do we learn range? Well, the range is a quick and easy way to get a general sense of the spread of the distribution. It is also easy for most people to understand, while standard deviations are not that easy for most people to understand without some training.

Why do we learn the sum of squares and variance? At this point in the book, the sum of squares and variance are simply important steps toward calculating the standard deviation. However, later on in the book you will see that both the sum of squares and variance are used in many of our inferential statistics, and we’ll go into that later.