Sure, there are such approximations, but having that information will not help you get the best price in a specific situation.
The variance in those approximations is significant, and vary based on many factors including the specific year, model, and options. In the end, the used car dealer has many other factors to contend with, including inventory and sales objectives.
If you really want to get the best deal, the first thing you have to do is to NOT get emotionally attached to any one vehicle (such as is indicated when you say, “I found a vehicle I like very much…”).
Understand that in most cases, you won’t get the best price from a used car dealer, since you will have to pay sales tax on the transaction (which, depending on where you live, could be a significant factor). Of course, you may find other value from buying from a used car dealer, such as some sort of warranty protection (which will probably cost you as well).
Find at least three cars that would meet your families need, and that you would be equally pleased with having. Build a spreadsheet with all of the major and minor options with each. Use a used car pricing guide, such as Kelly Blue Book and Edmunds, and calculate the wholesale and retail values.
Check out each of the cars, if necessary, but without discussing any price issues, other than the asking price. Once you have three cars to negotiate with, begin contacting the owner/dealer, and offer them a low-ball price for the car. You may want to start as low as the wholesale value. If anyone accepts your first offer, you didn’t go low enough. Don’t worry about being laughed at or “offending” the other party. If they don’t accept, see if they provide a counter-offer. Continue to the next car. Once you have three rejected original offers, and perhaps some counters, raise your offer price, and go back through the same routine. Continue until an offer is accepted.
ALWAYS do this over the phone. Never negotiate in person.
As in any negotiation, the other party will always come out ahead if they have more POWER, INFORMATION, or TIME, than you do. Don’t let them pressure you, make sure you pressure them. If they sense you are committed to a particular vehicle, you lose. If they sense you have little time to make a decision, you lose. If they sense you are unfamiliar with your Next Best Alternative, you lose (so feel free to tell them that you are negotating with two other owners of equally satisfying vehicles, to keep the pressure on them).
Hope this helps. Good luck.