If the data can be obtained quantitatively, one is on much more solid ground. However, some individuals do not clearly understand what numbers, graphs, or other numerically-based communication vehicles mean. Therefore, there are limitations to the use of numbers. In addition, unless a researcher acknowledges this point, he or she may interpret, e.g., a randomly checked numerically-based questionnaire, as real when it isn"t.
Actually I believe its depend on the problem. In predictive problems, if someone is interested in a selection problem (for instance identify the top 10) even using quantitative data we can categorize the response into classes, and use powerful classifiers, popular nowadays like deep learning models (Neural nets using categorical likelihoods etc). However, if one may interested in quantifying some reliable quantitative value, like incidence of cancer in some continent or country, quantitative analysis using hierarchical models can give high accurate results.
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Both are crucial. If a quantitative analysis is performed, but cannot be explained and interpreted, it is little more than an arithmetic exercise. A description is provided without support of quantitative analysis, it is little more than opinion.
as others have commented, it depends on the problem. also you need to understand the formula that is applied to analyze the data. remember the issue of garbage in garbage out. just because if in figures does not make it necessarily the most accurate.