Final answer:
The statement is true; data that can only take on whole number responses are referred to as discrete data, which are countable and take on fixed numerical values, as opposed to continuous data that can include fractions and decimals.
Step-by-step explanation:
The statement 'If the possible responses can only be a whole number, we refer to the data as discrete' is indeed true. Data are classified as either quantitative or qualitative. Within the quantitative category, data can further be classified as either discrete or continuous. Discrete data are countable values, which means the data can take on only certain fixed values. An example of discrete data would be the number of students in a classroom, which can only be expressed in whole numbers such as 20, 21, or 22 students.
Continuous data, on the other hand, are data that can take on any value within a range, including fractions and decimals. An example of this would be the measurement of time, temperature, or distance in which you might have measurements like 17.5 seconds, 22.3 degrees Celsius, or 100.8 miles.
Looking at the provided examples, we can identify different types of data. For instance, the number of pairs of shoes you own would be quantitative discrete as you cannot own a fraction of a shoe. However, weights of sumo wrestlers or the distances from your home to the nearest grocery store would be examples of quantitative continuous data.
In conclusion, when data consist of whole numbers resulting from a counting process, they are considered discrete, thus affirming the initial statement as true.