Final answer:
Discrete data is countable and typically expressed in set notation, while continuous data is measured and expressed using inequality notation. In probability, discrete data can have probabilities for individual values, while continuous data is discussed in terms of ranges, as single values have a probability too infinitesimal to measure.
Step-by-step explanation:
Whether an equation represents a discrete or continuous situation influences how the data is expressed. Discrete data consists of countable values, typically expressed in set notation or listed individually, while continuous data represents measured quantities and is often expressed using inequality notation to represent ranges of values.
For example, the number of books purchased is discrete and could be represented by the set {2, 3, 4} if you bought 2, 3, or 4 books. On the other hand, the amount of money spent is continuous, and could be expressed with inequality such as 20 <= x <= 100, representing spending anywhere from $20 to $100.
With continuous probability functions, you can't find the probability for a single value but rather for a range of values. For example, if P(x < 5) = 0.35, P(x > 5) would be 0.65 based on the complement rule. This is because continuous data can take an infinite number of values within a range, and the probabilities for the entire range must add up to one.