Final answer:
Quantile classification is the method that produces an equal number of cases in each class, unlike the natural break or standard deviation methods, which do not ensure equal class representation.
Step-by-step explanation:
The classification method that produces an equal number of cases in each class is known as quantile classification. While both the natural break and standard deviation methods are commonly used for classifying data, they do not guarantee an equal number of cases in each class. The natural break method, also known as Jenks optimization, focuses on reducing the variance within classes and maximizing the variance between classes, but does not concern itself with the number of cases per class. On the other hand, the standard deviation method classifies data based on how many standard deviations away from the mean they fall, which again, does not necessarily result in equal numbers of cases across classes.
Quantile classification, alternatively, divides the data into classes containing an equal number of cases. This method is useful when you want to ensure that each class is equally represented, which can be important for visual interpretations such as in thematic mapping. However, one downside to this method is that it can sometimes place very different data values into the same class if the dataset size requires it to meet the equal-case criterion.