Descriptive statistics are used to organize, summarize and describe the attributes of a set of data. A set of data, especially numeric data, are often referred to as a distribution.
A category of descriptive statistics is those measures that describe a distribution using one measure and can be thought of as describing “middle’ or typical score within a distribution. These measures of central tendency, such as the mean, median, and mode, are typically used as the best summary of a distribution of scores and often describe the “average” score. For example, knowing the average score on an exam would help us understand how the typical student performed. Knowing the average height in a population allows a comparison using your own height. Your height could be described as “above,” “below,” or “on” average.
Another category measures the dispersion or variability of scores within a distribution. The range, standard deviation, and variance describe how much scores with a distribution differ from one another. The standard deviation could be used to describe the variability of test scores in a class; the smaller the standard deviation, the more similar the scores are to each other
When combined, subcategories offer an easily interpreted summary of a data set and allow comparisons to other data sets. When a mean and standard deviation are reported together, they accurately describe the typical score and how spread apart these scores are from each other. These categories of descriptive statistics are used in more sophisticated techniques to compare sets of scores to determine if differences between the groups are “statistically significant.” More on that in future posts.