Batches of Numbers

Abstract

A batch is a set of numbers that are related to each other because they are different instances of the same thing. The simplest example of a batch of numbers is a set of measurements of different examples of the same kind of thing. For example, the lengths of a group of scrapers, the diameters of a group of post holes, and the areas of a group of sites are three batches of numbers. In these instances, length, diameter, and area are variables and each scraper, post hole, and site is a case. The length of one scraper, the diameter of one post hole, and the area of one site do not, together, make a batch of numbers because they are completely unrelated. The length, width, thickness, and weight of one scraper do not, together, make a batch because they are not different instances of the same thing; that is, they are different variables measured for a single case. The length, width, thickness, and weight of each of 20 scrapers make, not one batch of numbers, but four. These four batches can be related to each other because they are four variables measured for the same 20 cases. The diameters of a set of 18 post holes from one site and the diameters of a set of 23 post holes from another site can be considered a single batch of numbers (the variable diameter measured for 41 cases, ignoring entirely which site each post hole appeared in). They can also be considered two related batches of numbers (the variable diameter measured for 18 cases at one site and 23 cases at another site). Finally they can be considered two related batches of numbers in a different way (the variable diameter measured for 41 cases and the variable site classified for the same 41 cases). This last, however, carries us to a different kind of batch or variable, and it is easier to stick to batches of measurements for the moment.