Final answer:
A quantitative characteristic is measured using numerical values and can be either discrete or continuous. A discontinuous characteristic is qualitative and falls into distinct categories or groups.
Step-by-step explanation:
In mathematics, a quantitative characteristic refers to a characteristic or attribute that can be measured or counted using numerical values. This type of data is always represented by numbers and can be either discrete or continuous. Discrete quantitative characteristics take on specific values or counts, such as the number of pairs of shoes you own. On the other hand, continuous quantitative characteristics can have any value within a specific range, such as the distance from your home to the nearest grocery store.
A discontinuous characteristic, on the other hand, refers to a qualitative characteristic that cannot be measured numerically. Instead, it is characterized by distinct categories or groups. For example, the type of car you drive is a discontinuous characteristic because it falls into specific categories such as sedan, SUV, or truck. Unlike quantitative characteristics, discontinuous characteristics do not involve numerical measurements or values.