The best and only real tool for defining a customer avatar is speaking to actual customers in one on one interviews. There are so many ways to interpret data and misreading what it means that using any tool without speaking to customers can lead you in the wrong direction. Imagine that FB insights tells you that your audience is mostly single. Why are they single? Are they single and looking or are they happily single? This kind of information is not available in FB or any 3rd party platform.
Long before you create an avatar, you should have brainstormed all of the markets your potential solution or product might serve. You want to do this with the end users in mind. If you are targeting teachers, different segments would include primary school teachers, high school teachers, subject-specific teachers, special needs, you name it. To the extent they are likely to have different needs from a product or service, they are different markets. Most people focus on too broad of a market with too many types of end users.
Once you have a healthy list of possible markets, you want to narrow it down to the 6-12 that seem the most promising. From there, you want to conduct primary (first-hand) research by speaking to 3-5 end users from each market segment. Check out CustomerDevLabs.com for great info about how to conduct these interviews. Find out who seems to have the greatest need for a solution, can afford one, and is adjacent to other markets. You want to narrow your markets down to one beachhead that consists of only one type of end user. The market should be as narrow as possible but be sufficiently big that, if you captured 100% of the market share, you would surpass break even and have a full solution developed. This allows you to stay narrowly focused on a simple set of customers and get to the point that prevents startup death as easily as possible.
Once you know your beachhead market, you will interview several more customers and begin to compile the customer avatar. You will find out what they all have in common and what is different. You will find out where they congregate offline and online, how they speak about the problem, what their top priorities are when considering a solution, and much more. This kind of information would never be gathered by using FB Insights or something similar. You can only know it by talking to the end users.
Once you feel like you really understand the end users you will be serving in your beachhead market, you want to pick one actual customer who most exemplifies the end user. Literally, pick a customer who is the perfect customer for you, and then take the customer avatar one step further by finding out all of the details you can about this one person. Even things that seem irrelevant - what kind of car they drive, how to do they dress, where did they grow up? You want to know this customer like you know a good friend. As you think through product decisions, sometimes you will simply say, "Would Sam want this feature or find this value proposition compelling?" And, you'll often know the answer because you know Sam well. When you don't know the answer or there is internal debate, you will literally ask Sam for the answer. What they say is final.
This process is outlined in a book called Disciplined Entrepreneurship. I highly recommend reading it and doing this the right way. If you feel like chatting about it, let me know.