Statistical methods are very useful for learning about populations, which can be defined in various ways. We begin with the following definition:

Examples of populations include (1) all of last year’s graduates of Dartmouth College’s Master of Business Administration program, (2) all consumers who bought a cellular phone last year, (3) all accounts receivable invoices accumulated last year by The Procter & Gamble Company, (4) all Lincoln Town Cars that were produced last year, and (5) all fires reported last month to the Tulsa, Oklahoma, fire department.

We usually focus on studying one or more characteristics of the population units.

For instance, if we study the starting salaries of last year’s graduates of the Dartmouth College MBA program, the variable of interest is starting salary. If we study the gasoline mileages obtained in city driving by last year’s Lincoln Town Car, the variable of interest is gasoline mileage in city driving.

We carry out a measurementThe process of assigning a value of a variable to each of the units in a population or sample. to assign a value of a variable to each population unit. For example, we might measure the starting salary of an MBA graduate to the nearest dollar. Or we might measure the gasoline mileage obtained by a car in city driving to the nearest one-tenth of a mile per gallon by conducting a mileage test on a driving course prescribed by the Environmental Protection Agency (EPA). If the possible measurements are numbers that represent quantities (that is, “how much” or “how many”), then the variable is said to be quantitativeA variable having values that are numbers representing quantities.. For example, starting salary and gasoline mileage are both quantitative. However, if we simply record into which of several categories a population unit falls, then the variable is said to be qualitative or categoricalA variable having values that indicate into which of several categories a population unit belongs.. Examples of categorical variables include (1) a person’s gender, (2) the make of an automobile, and (3) whether a person who purchases a product is satisfied with the product.¹

If we measure each and every population unit, we have a population of measurements (sometimes called observations). If the population is small, it is reasonable to do this. For instance, if 150 students graduated last year from the Dartmouth College MBA program, it might be feasible to survey the graduates and to record all of their starting salaries. In general:

Often the population that we wish to study is very large, and it is too time-consuming or costly to conduct a census. In such a situation, we select and analyze a subset (or portion) of the population units.

For example, suppose that 8,742 students graduated last year from a large state university. It would probably be too time-consuming to take a census of the population of all of their starting salaries. Therefore, we would select a sample of graduates, and we would obtain and record their starting salaries. When we measure the units in a sample, we say that we have a sample of measurements.

We often wish to describe a population or sample.

As an example, if we are studying a set of starting salaries, we might wish to describe (1) how large or small they tend to be, (2) what a typical salary might be, and (3) how much the salaries differ from each other.

When the population of interest is small and we can conduct a census of the population, we will be able to directly describe the important aspects of the population measurements. However, if the population is large and we need to select a sample from it, then we use what we call statistical inferenceThe science of using a sample of measurements to make generalizations about the important aspects of a population..

For instance, we might use a sample of starting salaries to estimate the important aspects of a population of starting salaries. In the next section, we begin to look at how statistical inference is carried out.

Exercises  1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11