Bicycle race
Bicycle race. Source

Position

Our next measure is position. Position is a bit different than central tendency and spread in the following way. With central tendency and spread, we're asking a question about the dataset as a whole: what is the mean of the dataset, for example, or what is the range of the dataset? With position, we have a dataset, but we're asking a question about individual elements in the dataset: where do we "locate" a given element in the dataset?

A couple examples will make this clearer.

Example: Ranking U.S. graduate programs in Sociology

We might ask how the graduate program in Sociology at UC San Diego ranks among all U.S. graduate programs in Sociology. This is a question about a specific Sociology program rather than one about Sociology programs in general.

Example: Percentile scores on standardized achievement tests

Suppose that all 8th grade students in a certain state take a standardized achievement test, with possible scores ranging from 0 to 24. We might ask what percentage of scores falls below 21. This is a question about a specific score.

In the sections that follow, we'll consider three common ways to measure the position of elements in a dataset.