What do the real limits of a continuous variable represent?

The concept of real limits for a continuous variable relates to the range of possible values that represent the actual measurements on either side of a recorded value. In continuous measurement, values are not confined to discrete points but can fall anywhere within a range. The real limits are defined as the boundaries (upper and lower) that correspond to a given value. For example, if a measurement is recorded as 5, the real limits would be 4.5 and 5.5, effectively indicating the interval within which the true value could lie.

This understanding is crucial in statistics, especially when calculating probabilities or applying statistical methods such as histograms, where the representation of data is continuous rather than categorical. Recognizing real limits helps in accurately summarizing data and conducting analyses that involve continuous variables.