Don't you hate inane, lengthy Product surveys? They exist because someone hasn't thought enough about when to use qualitative or quantitative methods. Qualitative methods get the why and how answered before you can formulate the right quantitative questions.
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Customer interviews are the best way to uncover problems to solve. How do you know which of these brilliant new insights are the most valuable, the ones that will drive people to buy, the ones you should focus on first? That's where the quantitative survey comes in. You can learn how many potential customers in which segments are motivated by which of these problems (and begin designing solutions to them). The later survey can then be much shorter, to the point, and better crafted using the customers’ terminology and mental models.
Yes? What am I missing? Tell me a story.