This website is a good average: http://www.simplyhired.com/salaries-k-virtual-assistant-jobs.html
It’s kind of hard to say what a going rate is just because there are a lot of factors at play. First, there’s your experience level, then your office set up (those who have everything a brick and mortar office has are able to serve clients needs better), then you have what the job entails (if you are doing multiple different jobs you should be paid more), and there’s also what the client is willing to pay. A lot of clients are going to be people who are just starting out with there businesses and need help either seasonally or for a short period of time, these clients are going to pay less. On the other hand, there are clients who are big deals and need full time help doing various jobs and will constantly being adding on new things for you to do, these clients will pay significantly more.
When freelancing Virtual Assistant jobs the biggest thing to remember is to not sell your services too cheap. You may think that charging less then competitors will get you more jobs however that can backfire. A business owner doesn’t mind paying more for quality work and will skip over people who seem too cheap. Set your prices based on your experience, set up, hours you are willing to work, and the quality of work you are able to put out.
On another note, I have noticed you can make more by freelancing on sites like freelancer.com or odesk then you can working for an agency which places you with a client or the ones where you bid for jobs. While companies where you bid for jobs can be legit you will make way less then freelancing yourself out, some people don’t mind working for pennies a day.