Final answer:
Variables are characteristics that can be categorized as either categorical or quantitative. Categorical variables describe attributes, while quantitative variables represent measurable quantities, either discrete or continuous, and have specific units of measurement.
Step-by-step explanation:
In statistics, a variable is a characteristic, number, or quantity that can be measured or quantified. Variables can be categorical (qualitative), which means that they describe a quality or attribute of a member of a population, such as sex or handedness, and cannot be quantified in the same way numbers can. On the other hand, variables can also be quantitative, meaning they represent a measurable quantity with numerical values, such as height or distance walked. Quantitative data can further be described as discrete (if the data results from counting, like the number of yards) or continuous (if the data results from measuring, like height).
Here's a breakdown of the provided data descriptions:
Sex: Categorical
Height: Quantitative (with units in inches or centimeters, indicating continuous data)
Handedness: Categorical
Number of yards walked before going out of bounds: Quantitative discrete (measured in yards)
Direction of wandering off course (left or right): Categorical
For quantitative variables, appropriate units of measurement need to be used, and for categorical variables, categories need to be clearly defined.