Who is right, the marketing director or his boss? If you answered, his boss, what would you do to fix the measure of satisfaction?

You are approached by the marketing director of a local company, who be-
lieves that he has devised a foolproof way to measure customer satisfaction.

He explains his scheme as follows: “It’s so simple that I can’t believe that
no one has thought of it before. I just keep track of the number of customer
complaints for each product. I read in a data mining book that counts are
ratio attributes, and so, my measure of product satisfaction must be a ratio

attribute. But when I rated the products based on my new customer satisfac-
tion measure and showed them to my boss, he told me that I had overlooked

the obvious, and that my measure was worthless. I think that he was just
mad because our best-selling product had the worst satisfaction since it had
the most complaints. Could you help me set him straight?”

The boss is right. A better measure is given by
Satisfaction(product) = number of complaints for the product
total number of sales for the product