One of the more difficult issues facing you will be making sure you compare apples 'n apples while understanding the differences between apples 'n oranges.
Some things common to all:
How far from your (water) meter pit to the home?
Do you know what sort of water pressure you have?
Those two questions sortta drive the rest. How many sprinklers you have is a piece of the puzzle but it is lower on the issues list than how much water pressure and gallons per minute of flow (gpm) you have. Knowing the water pressure and gpm coming to the house is important because it is the info divided by the flow rate of the heads to tell you how many you can run at a time.
That, plus the number of heads it takes to cover your yard will let them decide on how many zones to cut the yard into (each zone is X number of heads that run at the same time).
Will the different estimates be for systems that are all parts from a single manufaturer or will it be a collection of brands? Some will tell you that the parts (controller, back-flow, heads and even specific heads) are better from different manufacturers while others will tell you that all from a single manufacturer will give you an optimized system.
And, are the contractors equally certified? Not only education and experience but certifications from the various manufacturers who's parts they want to use. And, will their installations be the same? Will they open trenches all around your yard and be a week getting the stuff layed, connected and back-filled? Or, will they pull the flexible pipe and be in 'n out in one day with water flowing to cover their intrussion before they leave that day?
Will your system need to be blown out with pressurized air at the end of the season to avoid winter freeze and bursts or will it drain automagically?
I know, I took your simple question and made it hard.
When I bought my system about 9 years ago, I had a variety of estimates and the differences sortta fell into the mess I listed above. The low estimate was a person who seemed to be from the "get it in the ground and fix it later" school.
The highest estimate was from someone who seemed more concerned about my yard and the final result than I was. The low person was using parts 'n pieces from a variety of manufacturers. The high person was certified by the company that made all the parts he was wanting to use and he carried a fairly high rating from them for his past performance.. He would vary for me if I wanted but he had sound reasons from the controller to each of the heads as to why he preferred his "brand".
It doesn't look like you are a member of Angie's List. Given the size of the investment you are looking at, this might be a great time to join and see how others in your community have rated the contractors you are considering or if there is one you should add to your list.
My yard is between 12 and 15,000 square feet less the house, deck, two mini-barns and it is interrupted with a number of blocking (blocks the stream of water) evergreens and planting beds.
The low estimate I had was about $2,500 and would take three days to put in from the time they began to trench. I don't recall how many heads he wanted to put in but if it was off, he'd be able to put another anyplace and tie it to the nearest zone to give me good coverage. Uh, this was the get it in the ground 'n adjust later person.
The high estimate I had was around $4,500. This proposal was for seven active zones each having 5 to 7 heads. There was enough capacity (extra zone controllers and space within the system controller) built in to add drip irrigation at a later date for the planting beds without having to replace anything. He drew the entire yard and gave me a copy with the heads marked showing the "throw" of each and the overlap he built in to avoid any missed areas. And, they wanted to arrive in the morning and leave that evening with the system watering to cover their tracks throughout the yard. One day and they would not leave until it was working as advertised!
I took the high estimate. I have a neighbor who bought from the other folks. Both of us are happy. He is really happy because each time he calls his company for adjustments or corrections (yep, they got it in the ground and are still putzing with it) they are out within the week, they are really easy to do business with and their service calls' costs haven't gone up a whole bunch.
Sorry, you can't look at the price and divide by X number of heads and have a fair comparison.