Variable

In a table arranged with one row per observational unit, each measurement column records a variable. The unit is who or what you measured, the variable is the characteristic you recorded, and the cell where they meet holds one measurement. The name does real work: a characteristic earns it only if its value can change from one unit to the next.

Three rows and three variables, the first column naming the unit rather than measuring it. Height and commute time are quantitative, so $\bar{x}$ (x-bar) means something: the mean height is $497 / 3 = 165.67$ centimeters. Lunch is categorical: counts and a most common value, no mean at all.

"The variable is 168." No. The variable is height, and 168 is the value height takes on student 1. In this table, the variable is named by a measurement-column heading, and a cell records its value for one student. The same slip in reverse counts the three students as three variables.

A variable may have no observed variation in a particular sample. If every student here is in tenth grade, grade level is still a recorded categorical variable, but it has only one observed value. This sample provides no between-grade comparison; that is different from saying grade level cannot vary in a wider population.

Topic 1.2 asks you to identify observational units, variables, parameters and statistics from a study, defining a variable as a characteristic that may change from one unit to the next. A numerical summary of a variable is a parameter for a population and a statistic for a sample. A random variable is a different object with a similar name.

That row-and-column picture depends on the layout. Repeated measurements can occupy several rows for the same individual, or several time-specific columns in one row; name the characteristic and unit rather than relying on position alone. In the descriptive statistics classroom activity, classify a packing order's identifier, station label, item count, and elapsed time before comparing the two groups.