I know that a particular product will be useful to a whole group of people. However, I am uncertain if once the product is made, the people will purchase the product.
Prior to making the product, how can one know (if at all) whether a product will sell?
The product I have in mind is a data analysis system that has not been implemented, or if someone has done it, it has not been popular. My target audience is academia (students and scientists) and perhaps research based companies that need to do data analysis.
Kudos for wondering about the right things before getting started.
You're probably not going to get the absolute you want, but here are the first things to check, in this order.
You can guesstimate how much your product will be worth to someone (or their employer) by figuring out how much their time is worth, in dollar terms, and multiplying by how much time your product will save them.
Based on that, I'd guess different groups will find different prices acceptable, and the general trend will be:
Companies > Faculty > Students
Carson McComas makes some great points, but the tricky thing is to find enough people to talk to to get a decent sample.
One popular way is to create a landing page advertising the product, making not just the features/value proposition of the product but also the pricing clear (eg. make sure that it's clear that it's not free and show your current thoughts on pricing) and provide a "sign up for the upcoming beta" form collecting email addresses. Put a hundred dollars or so into Google Adwords to drive traffic, and promote it as unspammily as possible elsewhere -- Tweet about it, if you're a regular participant in relevant forums then say there that you're working on it, that kind of thing. If you have a relevant blog, promote it there. You can probably think of many other ways.
Email the people who sign up, and engage them in conversation (if they're willing to reply). Make sure that they really are willing to pay. If it feels OK (from the conversation you're having), discuss the pricing options you're considering, and ask for their thoughts. Also discuss feature sets and possible future directions if you want, this can give you a better idea of your potential market and might change your mind about the shape the product should take. Ask them what they'd do with it, perhaps they'll surprise you!
If it turns out that everyone says "cool, but I'd never pay for it", you can always discontinue the landing page and (if you feel it's appropriate) drop the people who signed up (or at least those you were corresponding with) a note saying "sorry, there wasn't enough interest".