Measures of variability, such as the range, variance, and standard deviation, are types of descriptive statistics that complement the measures of central tendency in describing data sets. These measures of variability reflect how scores differ or are spread or dispersed from one another. A more precise definition is the distance or amount a score in a data set differs from the typical score in the set, usually the mean.

The three most common forms of variability are the range, variance, and standard deviation.

The range is the distance between the highest score in the set and the lowest score in the set. It is the easiest to compute but also the least precise.

The standard deviation is the average amount that each score differs from the mean of that score set. It’s the most commonly used type and has inferential and descriptive statistics applications.

The variance is the square of the standard deviation. Variance also has applications in inferential and descriptive statistics.

These measures of variability are foundational to advanced statistical analysis techniques as they generally represent “error”; this should not be confused with inaccuracy or a mistake. It is the naturally occurring differences we expect to see among research participants anytime we measure numeric data. We know that not all people have the same exact characteristics or the same responses to situations or interventions, so individual responses or differences are expected. To understand data in more advanced analyses, we must measure and understand those differences. One of my statistics professors regularly said, “statistical analysis is all about variability.”