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Qualitative assessments apply practitioner expert judgment based on the best available data.  These analyses commonly use terms such as high, medium, or low to communicate an approximate range of the hazard posed by a type of event.  This approach is useful when insufficient information is available to develop a detailed quantitative assessment, or when the relationships between the various parameters cannot be reliably established. 
Quantitative assessments have the advantage of providing numbers that can be used to express outcomes.  Even if the numbers are used to develop broad categories such as high, medium, and low, the presence of numbers adds a comforting sense of exactness to what is essentially a vague process.  Quantitative approaches should be regarded with caution; the history of disasters is full of events that were not identified in their actual form by the best analytical tools of the day.