Is there a way to adjust the +/- accuracy to be greater than just 1 degree on the Honeywell RTH230B thermostat?

We have it in manual mode set at 72 degrees. It stops cooling at 71 degrees and starts cooling just before it reaches 73 degrees. Ideally, we'd like this range to be greater... like not starting to cool until it reaches 75.

We also don't understand how the cooling cycles work.

Thanks in advance for any help!

Move the set point to 75 degrees then it will maintain that temperature. If you are looking for a wider band you should have bought a cheap Hunter thermostat because they are inaccurate to start with. Honeywell is a pretty accurate thermostat and most people do not want a wide swing like from 72 to 75 and then back to 72.