Which of the following methods categorizes data without predefined intervals?

The method that categorizes data without predefined intervals is the Natural Breaks method. This technique, also known as Jenks optimization, focuses on identifying natural groupings within the data. It works by minimizing variance within classes and maximizing variance between classes, allowing the data to determine the best way to be grouped based on its inherent distribution.

Natural Breaks is particularly useful when the data has clear clusters or patterns, as it allows for the establishment of categories that reflect the actual structure within the data rather than imposing arbitrary intervals. This flexibility results in a more intuitive and meaningful representation of how the values are distributed across the study area, making it a valuable choice for a variety of GIS applications.

In contrast, the other methods mentioned involve assigning data to categories based on set parameters or criteria. Quantile divides the data into equal-sized groups, defined interval establishes fixed ranges, and equal interval creates categories of uniform size. These approaches do not adapt based on the specific distribution of the dataset at hand, which is why they are not suitable for categorizing data without predefined intervals.