Statistical Inference: A Short Course

1.2 The Population and the Sample

The concept of the “entire data set” alluded to above will be called the population; it is the group to be studied. (Remember that “population” does not refer exclusively to “people;” it can be a group of states, countries, cities, registered democrats, cars in a parking lot, students at a particular academic institution, and so on.) We shall let N denote the population size or the number of elements in the population.

Each separate characteristic of an element in the population will be represented by a variable (usually denoted as X). We may think of a variable as describing any qualitative or quantitative aspect of a member of the population. A qualitative variable has values that are only “observed.” Here a characteristic pertains to some attribute (such as color) or category (male or female). A quantitative variable will be classified as either discrete (it takes on a finite or countable number of values) or continuous (it assumes an infinite or uncountable number of values). Hence, discrete values are “counted;” continuous values are “measured.” For instance, a discrete variable might be the number of blue cars in a parking lot, the number of shoppers passing through a supermarket check-out counter over a 15 min time interval, or the number of sophomores in a college-level statistics course. A continuous variable can describe weight, length, the amount of water passing through a culvert during a thunderstorm, elapsed time in a race, and so ...